There are no doubt plenty of "nasty lefties", but ymb is sadly mistaken if he thinks it's only (or predominately) that way round. At a guess, it's because there's more reason to pay attention when it's "your side" under attack than when it's "your side" doing the attacking.
When Hillary Clinton was sick with pneumonia during the 2016 campaign, Trump was publicly mocking her. When Justice Ginsburg died recently, many right-wingers were celebrating and suggesting that they'd prayed for her death.
I don't understand this mentality, wherever it comes from, but it is not confined to the far left, nor is it primarily from that side. The political distribution of unfeeling, callous pricks is uniform.