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You can say:

[1] You can use any pen to fill out this form.

But people say you can't say:

[2] I meet any man of the group.
[3] I met any man of the group.

I wonder why you can't. To me, with [2], you have a good intention of seeing any man that belongs to the group who wants to see me. Or, this describes your inclination. [3] is just the past version of [2]

Why can't you say the two sentences alone.

Your first answer:

We use "any" for indefinite quantities in questions and negative sentences. We use some in affirmative sentences:

Have you got any eggs?

I haven’t got any eggs.

I’ve got some eggs.

Not: I’ve got any eggs.

Second answer:

We use "any of" to refer to a part of a whole:

So,

" I meet any of the men of this group ."
Or
" I meet some of these men...."

Similarly:

You can't say:

Are any man going to the meeting?

Correct one will be:

Are any of you going to the meeting?

[2] and [3] has no sense because these phrases are in Present Indefinite Tense. It's about what you usually do and not about you CAN do.
You can say:

I can meet any man of the group.

Or you can say (if it's about you):

I meet every man of the group.