One big reason is wet handling characteristics. The tread patterns on the front and rear tires are designed to work together in terms of how they channel the water. Matched tires are supposed to be less susceptible to hydo-planing. That said, I have run mismatched tires in heavy rain and didn’t have any problem.
Yoko Avid Ascend on rear radial ct, rear E3 Dunlop bias ply rear tire on front. Not sure you can get more different than this. Rides, handles great in all conditions and at all speeds ! Don't be skeered !
Factory Dunlop on rear, with Avon Cobra on front for wet weather. IMO to me on my bike this is a flawless setup. Living in the Rockies I have put them to all the condition we have here. No issues at all. I would just ad in just don't go cheap on tires. If you have a HD cost of tires are nothing. Be safe, ride smart.
Running a Yoko Avid Ascend 195/60/16 on rear and an E3 Dunlop 180/55/18 on front. Hard to get much different than this. Ran an Avon Cobra 180/55/18 on front two years ago (bottom pic) , the E3 works better with the ct.
Interesting, more guys running different skins than I thought! Too many years riding sportbikes, it was the cardinal sin...
And there you have it. Also the reason so many think you can't run a car tire. They don't realize you will hit hard parts of the bike way before lean angles will give you a problem with the tire.