They really are so nearly synonymous as makes no difference, but I suspect your instructor may be cautioning you away from trying to be too witty or clever. "Pithy" is frequently misunderstood that way (to the point where it might be simpler just to admit that as one of its meanings), and it occurs to me that either your instructor might understand it that way or - follow me, it's a little convoluted - might have assumed that you meant it that way.

They both require brevity. But "pithy" suggests more rhetorical power for its length.

"Think for yourself" is succinct. "Don't follow leaders" is pithy.

The Merriam-Webster usage guide says:

succinct implies the greatest possible compression (a succinct letter of resignation).... pithy adds to succinct or terse the implication of richness of meaning or substance (a comedy sharpened by pithy one-liners).

So pithy is succinct and apt.

Yes, pithy definitely connotes well observed, witty, clever, spot-on ...the instructor is probably trying to steer you away from working hard to be clever, possibly too hard, and instead to focus on being clear, readable, and not overly verbose.

I think your guy was saying you went on too long.

Succinct = Norp Norp.
Pithy = Norp.

Ever tasted the white stuff on the inside of an orange peel? I think the bitterness is carried over into the flavor of the synonym, perhaps sweetened with a squeeze of juicy wit.

I think Miko has it. Thanks y'all.

Not much.