Um, you tell the op to get over himself, etc, but you admit that you considered or almost said ""giving up now? I have 2 more loops." How is that (talking trash) any better than racing the guy? (yes, you didn't say it, but you almost admitted that in the past you've said things like that, correct?)
Look, lots of people are jumping on the OP. Here's my 2 cents:
1) if your run is supposed to be an easy day, run your pace and don't get up with what others are doing. That is the smartest and maturest policy obviously. Racing people when you are supposed to be taking it easy just for an extremely temporary ego boost is, yes, silly and counterproductive. However..
2) this is easier said than done for many. Running is a very competitive sport. Humans are very egoistical in general. Put the two together, and of course people are going to challenge each other. And if the runner(s) in question don't have a lot of races in their future, or specific goals they are shooting for, maybe for them, "beating" the guy who passes them one day on the river (or in the park, or whatever), is all they have to get their juices flowing. It's just reality.
3) and yes, the OP complained about the "jogger" speeding up, but then he sped up too, so..... yeah, they were both basically doing the same thing (racing). I've been on both ends of that relationship. And no, I am never happy with myself when I get caught up in something like that, unless I was planning on running hard. But it happens to most people at least a little. If you were planning on running hard, then there is nothing wrong with a a little "race simulation," right?
4) to avoid this problem, I run a lot in areas where I am all by myself. Then I entirely run my pace. Know thyself.