The former proclaim Christ out of selfish ambition, not sincerely but thinking to afflict me in my imprisonment. (Philippians 1:17, ESV)It is important to notice that this particular group of people are still proclaiming Christ. There is no hint of a false teaching or of false teachers in this passage. When the teaching is false, Paul also responds quite fervently against both the teaching and the teachers of false doctrine. But in this case, he still maintains joy that Christ is being proclaimed. The problem, in this case, is not the message, but the preachers of that message.
These other preachers, instead of being motivated by a deep love of the apostle, are actually out for themselves. Quite possibly, they have seen Paul's imprisonment as an opportunity to jump into the spotlight themselves, and if they can put Paul down... take it permanently.
It doesn't matter to Paul. The Gospel is being preached. I wonder if I would have the same attitude?