What does the phrase that 'I've all but..' mean in this sentence?
Solution 1:
It means
I've almost but not quite given up dating ...
The All but part suggests the speaker has done everything.
But the expression is used when the speaker can't think of anything further to do, so it might not be literally everything.
Solution 2:
The relevant part of the sentence is "I've all but given up X". The speaker is saying that he is extremely close to giving up dating because of the "pain and humiliation", but hasn't done so.