When using "though", one is taking about something known, and adding a statement about something that would not normally be concluded from that fact.
- Though I recruited him, I do not like him.
- You know that I recruited him, but don't let that lead you to think that I like him.
- Though I do not like him, I recruited him.
- You know that I don't like him, but I didn't let that stop me from recruiting him.
In both cases, "I do not like him" and "I recruited him" are ideas that many people wouldn't normally associate with each other. The use of "though" allows one to tie them together.
In this case, the speaker is making it explicit that the two independent concepts, being likeable and being competent, are not being conflated.