I’d prefer to make the bullied feel welcomed than the oppressor with what limited time and resources I have

Nobody truely is solely the bully or bullied. That’s what seperates empathy from parochial empathy: understanding not only people who you like, but also those who you don’t like.

your link says that people who are ostracized by others tend to continue that cycle not that people who ostracized others were themselves victims of ostracization

You might misunderstand the meaning of the word cycle?