The continuous form is used to state or ask what was, is or will be happening at a given moment. So, if you call your friend and ask: What are you doing? she may answer: I'm playing cricket (for example, she is standing on the boundary with her phone in her pocket when you call).
If you tell your friend that you intend to call her around 7pm tomorrow, she may reply: Sorry, but I'll be playing cricket. In other words, around the time that you plan to phone, she will be on the cricket field and unable to take your call. (The simple future I will play cricket is not possible in this context.)
In the passive form, the object is made the subject or topic of the sentence. So in a context where sports are the subject of discussion, the passive is just about conceivable.
Which sports will be being played after school tomorrow?
Cricket will be being played by me.
Tennis will be being played by John.
Badminton will be being played by Mary.
But as Parrott in Grammar for English Teachers (p336) states:
Some people dislike putting two forms of be together (e.g. be being or
been being) ... They avoid standard passive constructions in the
future continuous or predent perfect continuous.
Perhaps you could ask your friend why he or she changed your perfectly usual statement into one that would be perceived by native speakers as extremely odd. It would also be useful to link to the BBC English page referred to in the question.
Best Answer
The future perfect continuous is actually
Your sentence
makes the sentence a passive construction: the future perfect continuous passive. You can also say 'progressive' instead of 'continuous'. This uses
will - modal
have - perfect
been - continuous or progressive
being - passive
eaten - main verb
This is grammatical, but rarely used–even in writing. The chances of someone saying it are infinitesimal. Your teacher probably demonstrated this construction because it demonstrates all the possible "characteristics" a verb might take on, including a modal.
This is a passive construction due to being. The subject apples is being acted upon by the agent him.
A sentence more likely to be encountered in authentic English does include the progressive. This is the future perfect passive:
as in
The use of the progressive (or continuous) being stretches put the action so that it has duration and can be represented by ~~~~~~~~, but the use of the progressive in combination with the future perfect passive is rare. Few people, beyond linguistic professors, are ever going to need to express