There are usually two reasons why someone would want to switch lanes with you:
The champion they are playing against counters them and staying in the lane could actually be bad for your team. In this situation I would usually switch unless I was doing very well in my lane.
The second reason is that the player they are playing against is just better than them at the game, which is usually the case. In this situation you do NOT want to switch lanes. Why? Firstly, this person has picked his/her primary or secondary role as this lane, not you, and it's possible that others could do even worse. Secondly, all you need to do is make more effort to Gank the lane and put huge pressure on the enemy, the jungler should be doing this anyway and if the opponent is able to consistently kill the jungler as well you're pretty much done anyway.
Hope this helps!