Losing Draw Offers

Often when I have an opponent totally whipped, he offers a draw before abandoning the game. Should I take that as an insult? I can't imagine why he would think that I would jump at the chance when I have a massive material advantage (queen+) or an obvious mate in one.

Maybe not an insult, more like a friendly gesture.  I told my son to accept all draw offers when playing non-tournament games (e.g. club, online, with friends, etc.).  I learned this when this happened with my son:

Son was playing against a 5 yr old at non-rated tournament; son is 6, so you know how they are: can't get beaten by a "baby".  Anyway, son made a really bad move and immediately wanted to take back him move, the 5 yr old said "no takebacks".  Son was on the verge of tears, and the 5 yr old offered him a draw.

I was really impressed with the 5 yr old (and how well his parents have taught him at good sportsmanship).  We are trying to teach our son that.

The situation that the OP is describing is the opposite of the one you mentioned -- it's definitely not "a friendly gesture" for someone getting crushed to offer a draw to the one crushing them.

Maybe they offered the draw as a joke, or as a last-ditch shot at avoiding a loss via the OP accidentally hitting the 'accept' button, or something, but it definitely wasn't a "friendly" act.

Because it saddens me that chess players have become such horrible people. It isn't just the draw thing. Also the violent threats, homophobic rants, cheating, the whole nine yards. I've been playing chess for over 40 years and recently, for the first time, my opponent threatened to sodomize my children with a broom handle. I have never seen someone swear at his opponent and storm out. If he had then the TD would make sure he didn't play in any future events.