Learn English – The word ‘not’ often doesn’t mean total negation in mathematical sense

The best way* to negate the construction, used to be, is to simply use never and replace the infinitive form of the verb with its past tense. Thus:

• I used to be a chain-smoker / I never was a chain-smoker
• This place used to be a library / This place was never a library
• He used to be such a decent plumber / He never was a decent plumber

It is also correct in some situations to say never used to:

• We used to go there / We never used to go there

In this case, never used to usually serves as an emphatic negation of something previously stated.

Your example, I used to be, is best negated as I never was/I was never, although, I never used to be and I didn't use to be (grates on my ears!) are also options, depending on the context. For instance:

• I never used to be like this!
• Things never used to be this way.

Also consider the following:

• You used to be such a good friend
• I never was a good friend.
• No, I never used to be.

Another similar set of examples:

• You used to fall sick all the time.
• I never used to fall sick all the time.
• I didn't use to fall sick.
• I never fell sick at any time!
• I was never sick.

You should always be able to determine the correct negation to use, as long you keep the definition of used to in mind:

describing an action or state of affairs that was done repeatedly or existed for a period of time in the past

— New Oxford American Dictionary (2nd Edition)

I didn't used to is strictly ungrammatical, though widely used informally or colloquially. (The correct form is didn't use to, although this is also very informal.) Using the past tense of another verb after didn't, in this case used, is grammatically incorrect. Consider this and other similar verb constructions:

• used to be : didn't used to be [Wrong]
• had to have : didn't had to have [Wrong]
• seemed to know : didn't seemed to know [Wrong]

Now, the problem with these examples can be rectified by converting the past tense to the infinitive:

• used to be : didn't use to be [Correct, but not widely accepted]
• had to have : didn't have to have [Correct]
• seemed to know : didn't seem to know [Correct]

Also, did not/didn't always precedes the infinitive form of the verb it helps:

• didn't go [didn't went? — No way!]
• didn't help [didn't helped? — No way!]
• didn't matter [didn't mattered? — No way!]

Here is a note from NOAD to back me up:

Usage

1 The construction used to is standard, but difficulties arise with the formation of negatives and questions. Traditionally, used to behaves as a modal verb, so that questions and negatives are formed without the auxiliary verb do, as in it used not to be like that and used she to come here? In modern English, this question form is now regarded as very formal or awkwardly old-fashioned, and the use with do is broadly accepted as standard, as in did she use to come here? Negative constructions with do, on the other hand (as in it didn't use to be like that), although common, are informal and are not generally accepted. 2 There is sometimes confusion over whether to use the form used to or use to, which has arisen largely because the pronunciation is the same in both cases . Except in negatives and questions, the correct form is used to: we used to go to the movies all the time (not we use to go to the movies). However, in negatives and questions using the auxiliary verb do, the correct form is use to, because the form of the verb required is the infinitive: I didn’t use to like mushrooms (not I didn't used to like mushrooms).

— New Oxford American Dictionary

*(in my opinion, that is)

As ruakh and Barrie have pointed out, but is a coordinating conjunction. Logically, it means the same as and, unlike the other coordinating conjunction, or, which is quite different.
The difference between and and but is not logical or even semantic, but rather pragmatic.

If A is true and B is true, both conjoined constructions in the set {A and B, A but B} indicate this fact. However, A but B carries in addition a presumption to the effect that the speaker did not expect B given A, or believed that A's being true would normally contradict B, or was for some other reason surprised that B is true in this context.

There is no special technical term to denote this except, possibly, contrastive. It is not, however, negation, of any sort.