This version of the Summaron 35mm came out with the M3 (in 1954 - the earlier LTM version was available from 1948) and was designed to be used with that camera using an accessory mounted 35mm viewfinder. In other words it predates the M2 (which came out in 1957) by up to three years.
I have one which I used to use with an M3 but never tried mounting it on an M2 (as I never owned one). I have used it on later cameras with success - in my case both an M4P and an M8.
Of course the Summaron does not bring up the 35mm framelines on any of these (as the M3 for which it was designed never had 35mm framelines). I can confirm that it also mounts properly on the later cameras as you say. And I can confirm that the lens can be easily adapted to bring up the 35mm framelines on those cameras that have them. I have not bothered as it's easy to use the frame selector on the cameras if required.
I must admit I had no clue that it might not mount on the M2 (???) and unless this is some kind of idiosyncratic feature of your specific lens (or M2 body) I would think it may have something to do with the way the lens indexes (or fails to index, more to the point) with that camera's rangefinder follower. However I have heard no mention of this and when I checked my copy of the Leica Pocket Book it makes no mention of it either. I am inclined to think it is more likely to be because there is something slightly "out" on your lenses mount or that of the M2 on which you tried to mount it.
Have a search through this selection of posts from the LEica Forum. There may be something there...... https://www.google.com/search?q=summ...IoBDAAegQIBBAN