It's not really paradoxical that 'showing weakness is a form of strength'. It's common for short-term and long-term concerns to conflict in this way.
Avoiding showing weakness protects us in the short term but leaves us without support in the long term. We tend to learn to do this early, so turning the reflex off is hard.
Turning it off when it's OK to do so both requires strength & makes us stronger over time.
-- wise words by @enkiv2 when he was over at weirder.earth