Dịch - Bulgarian-English - гордостта на човека ще го смири,а смиреният ще...

I'm not sure if I understood this line

Does it mean:

"Man's pride will humble him and the humble one will obtain honour" ?

Yes, is it so different that it can't be understood, Lili?

I was not sure if it was about a single man or "man" in a general sense (mankind)

It is not clear, more probably it's the mankind that's meant.

Ok...allow me to interrupt a bit here.
How come that "Man's pride will humble him"??
When someone acts out of pride doesn't he behave a bit arrogant? I don't know...

Yes, you're right, Jaq! I was astounded too by this pseudo-wisdom, but this is exactly the meaning of the phrase as it is.