Selected group doesn't become Mouse1 - there's a common misconception among players of the Mechwarrior games that Mouse1 = Group1... But it's actually by default bound to "Fire Selected Group" - there is no button for "Fire group 1"
Well...fix it! It makes no sense to keep it that way and on top of that only confuses the newbs.
The only advantage I see is selecting a group in chain fire mode, then using mouse1 to chainfire and mouse2 (or whatever the selected group is on) to groupfire

You can fix it yourself by editing the actionmap, just bind mouse1 to group 1.
Or use the actionmap editor if you can't be bothered to change the xml file directly.
Again: You won't get groupfire that way as it currently only works with fire selected weapon, but that will probably change at some point.