The peroxide-rich martian surface, and the intense UV radiation,
would tend to break down methane, not create it.

Also, surface chemistry for generating CH4 would require several assumptions.
Yes! Chemistry labs have created methane by nonbiological means, but NOT
under martian conditions.
I prefer to follow Occam's Razor on this one: The methane is either of volcanic [geothermal],
or biological origin.

By the way! The Mars Express scientists deduced the amount of methane in the martian atmosphere to be....about 10 parts per billion.
10 parts per billion is not a heck of a lot.

Jacob

"This planet has a 100 percent mortality rate."