downshifting to hard and to much is bad..and as far as skipping gears..if your just riding not racing or showing off then it should be cool..i used to do it ever now and then...
YES, downshifting and skipping a gear is bad
YES, upshifting and skipping a gear is bad
YES, BOTH upshifting and downshifting and skipping a gear is bad
NO, it does not harm your transmission in any way as long as you don't jam it into gear
downshifting to hard and to much is bad..and as far as skipping gears..if your just riding not racing or showing off then it should be cool..i used to do it ever now and then...
You know better; next time will be a ban.