No, the phrase will ever be does not include the past, but the statement your friend has made is perfectly correct and grammatical.
To explain:
Right now you are the oldest you have ever been.
This is true, unless you are a time-traveller, or your aging process goes backwards. I believe neither of that is true, therefore the statement is true.
Right now you are the youngest you will ever be.
This is also true, because you will never be any younger anytime in the future than you are right now at this very moment.
Imagine a timeline starting at right now, ending in the infinite future. There is no past on this imaginary timeline. At which point, on this timeline, are you the youngest (you will ever be)? At its beginning = right now!
EDIT: Seeing from the comments below your confusion, I'll try to explain this problem a little bit further.
Imagine the following sentence:
Will you finish this project?
This sentence may be expanded to:
Will you, in the future, finish this project?
Since will is a future tense and the future is already implied in it, there's no need for the expanded sentence.
As you mentioned, ever means "at any point in time," which is correct, but let's add it to our sentence:
Will you ever finish this project?
And let's expand our sentence again:
Will you ever, in the future, finish this project?
So, as you can see, ever still means at any point in time, but time is limited by the tense used in the sentence. Therefore, contrary to what you may or may not believe, will ever be does not include the past.
You raise a valid concern. On the one hand, we often talk of periphrastic tenses (and other constructions); on the other, some insist that a tense should be confined to a single word. Others, again, hold that tense is a property of a sentence or clause, not of a word or phrase. Can this problem be solved at all?
The short answer is: there are different models; some models are incompatible with certain other models; and we are free to choose whichever model we prefer. The term periphrastic tense is useful in a model that allows for tenses that consist of more than one word, but not in a model that doesn't. The definition of "tense" is not an objective fact that exists independent of human analysis: it is ultimately a label of convenience created by the observer. Both kinds of models have merit.
Most language users happen to think of will do as the future tense. Some linguists use other models. There is no consensus, not even among linguists, about what constitutes a tense.
Even word boundaries are not objective facts
Perhaps the most fundamental issue you raise is that of word boundaries. What were once considered two separate words may fuse into a single, new word, as in cantare habeo => chanterai. At some point in its development, the status of this phrase-or-word must have been uncertain. This shows how relative the whole terminology is.
But in most cases, a reasonable case can be made for either one or the other, so that the fundamental issue temporarily recedes to the background; it should be noted, however, that what we consider a "word" is to some extent intrinsically subjective and a matter of convention. It is just a convenient demarcation. But let's move on.
Is tense determined by form or by function?
Let me illustrate the problem by means of Latin, where terminology has been fixed for a long time. Tense comes from Latin tempus, "time"; part of the oldest concept of tenses had to do with notions of time. However, there was never a one-to-one correspondence between tenses and temporal references. The pluperfect, for example, is normally used to refer to a time before a narrated time in the past, just as in English; and yet after postquam, "after", the perfect was used, not the pluperfect. Similarly, the imperfect and pluperfect could be used to refer to an hypothetical situation in the present, as in English if I was rich... (although subjunctives were far more common). And so on.
Si domi eram, pater me puniebat. = If at_home I_was, father me punished. "if I were at home, father would punish me."
Postquam Galliam vidi, vici. = After Gaul I_saw, I_conquered_it. "After I had seen Gaul, I conquered it."
And yet we still call the verbs in these examples imperfect and perfect, respectively, even though they do not have their usual temporal references. The reason we do this is that the form is named after its most common function, even though it can indeed have other functions. Latin and English do this and are by no means the only languages.
Do we then look only at the form of the verb, not at its function, when defining tenses in Latin? No. What we call the passive perfect is periphrastic/analytic/compound, just as in English:
Canis sum. = Dog I_am. "I am a dog."
Visus sum. = Seen I_am. "I am/was seen."
You could say this is not a special tense, but two words, one being a past particple, the other a present verb; and yet this is called the passive perfect. The reason is that it functions just as the perfect does—except that it is passive. Here function determines what we call it. This happens in English too when we say I will do it is in the future tense.
Humans like symmetrical systems
So then what constitutes a tense, if we can count neither on form, nor on function, at least not reliably so? The answer is probably symmetry. If there is a present active (video "I see"), a present passive (videor, "I am (being) seen"), and a perfect active (vidi "I saw"), we would like there to be a perfect passive. Because there was no such verbal form, a phrase was made to be equivalent, (visus sum "I was/am seen in the past"). We humans like our systems neat and symmetrical if possible:
Active Passive
Present video videor
Imperfect videbam videbar
Perfect vidi [visus sum]
Future videbo videbor
Now is this label "passive perfect" merely a convention? It may have been once, but, as people start believing in it, they start using it in ways that neatly fit the system, even if the meaning of visus sum was once somewhat different. It is in some ways a self-fulfilling prophecy. Whenever a sentence in the active perfect was passivated, instead of saying "oh, I can't do that", people started thinking, "this is the passive perfect; I will use it". The same applies to I will do it in English.
All three approaches have up-sides and down-sides
Is this a perfect system of terminology? No. There are serious disadvantages. But it has been in use for a long while, and most people think of "I will do it" as fitting within a neat system of past, present, and future, because that is the most convenient and obvious partition of our verb tenses, or so we feel.
Various branches of linguistics have proposed different systems and different terminologies in the past. This is a productive and beneficial approach. Some chose to focus on form and consider the English periphrastic future not a tense at all; they will only count affixes and endings as capable of forming tenses. This system certainly has merit.
Others have emphasised function; they have gone so far as to declare that, since many forms can be used for more than one function, as with si eram... / "if I was...", only foregoing form altogether leads to a consistent approach. Hence they treat tense as a property of a clause or sentence, not of a word or phrase. That way, only combined with a word like yesterday does was acquire a past tense; in if I was at work today, you wouldn't see me here, it is a present tense, because it refers to a situation in the present, be it an hypothetical one. This approach, too, has merit.
One could use several systems at once
As an alternative, we could invent new words for these two new approaches, such as *single-word tenses for the English simple present and simple past, and time-reference or temporality for the time-reference of a clause or sentence. Many different models are possible. Insisting on one model without considering the benefits of other models seems unwise. And saying "x is A" when you mean "I find the model in which x is called A most useful" is a simplification.
Suppletion as an illustration of a convenient choice
Some systems are uncontested, even though at some point in the past a fairly arbitrary choice must have been made.
I go.
I went.
Do these two forms belong to the same verb? Yes, you will, say, because that is what you were taught, and because they "feel" like the same verb, just with odd forms. But, in the past, there were two verbs, both meaning something like going (although there were no doubt some differences between them). At some point the present form of a verb resembling go was taken, its past forms discarded (or not, if such never existed), and the past form of a verb resembling went.
We could say, "there are two defective verbs in modern English, one lacking a past form, the other a present form"; but we choose not to do so. That is to some degree arbitrary, but in this case it is just very convenient. If certain linguists would prefer to treat them as two different verbs, then let them do so, if this is somehow more convenient in a certain linguistic analysis. Or they could just say "this verb consists of two different roots", as they no doubt do.
Best Answer
English has no future in the future because English has no future tense at all. English verbs approach tense from two perspectives: before now (past), now and after now (present/nonpast). As such, we can conjugate the verb to eat as follows:
But there is no way to conjugate the verb for the future, and so we resort to periphrastic constructions to form future aspects, which, for better or for worse, usually infuse other meaning into the sentence:
These all imply future time (and thus form the future aspect), but may infuse undesired meaning into the sentence. Nevertheless, we also have less meaning-rich, albeit more verbose, ways of expressing future time:
So, although there is no future in the future tense, we can form a future in the future aspect by combining the foregoing constructions:
Both of which sound fine on occasion, but may grate on the ears (eyes) if heard (read) too often, especially in the passive voice: the food will be going to be eaten.
It is also worth noting that the present tense is often used for both present and future time, often making the future aspect seem too verbose where it is still grammatical. Consider the following pairs:
In each pair, both sentences mean about the same thing and, at least where I live, the average Joe is more likely to say the first. This is merely something to consider, however, and it is not meant to discourage your idea at all.