How to Effectively Sink a Ship

So I'm trying to get across to the audience that a relationship is bad. Basically, one of the people in the relationship is shallow and is primarily interested in maintaining their social status. The thing is, other than being a social climber, this character is a fairly decent person. I've even given them a few Pet the Dog moments. I can easily see this character and relationship developing a misaimed fandom. Is there a way I can make it clear to readers that these two shouldn't be together?

It's hard to give advice when we only know details about one of the characters. Tell us about the second one?

That said, you could always hit the audience over the head with a sledgehammer by having the characters mutually agree that "No, we wouldn't make a good couple."

Bear in mind that you don't have full control over how your readers perceive your characters: whatever you write, there may well still be a portion of your audience who wants the characters to be together.

That said, perhaps show the relationship being problematic; consider what you find objectionable about it, and include scenes that show or reference those things.

I would say the other person in the relationship is a bit weak-willed. If their friends were going to do something they didn't want to do, they would go along with it anyways. They're very averse to conflict and would pretend to get along with someone so as to avoid a fight or argument.