The honor system progresses based on the following things:
- Play a LOT of games
- Don't get validly reported
- Get honors
- Get team honors bonus.
Most people that are progressing in honors trip on point 2, where valid reports (even for mild toxicity) puts your progress to a screeching halt.
My advice to you, avoid things that can get you validly reports such as:
- asking/threatening for reports
- claiming they are done, it's gg and threatens to afk
- calling others noob / kid
- KDA / rank shaming
If you want to move forward in honors faster, try to encourage your team more. Compliment them after good plays, pick them up if they are getting tiled and make recommendations, but don't force people to play your way.