That is completely bullshit, especially after last chapter which established he wouldn't be willing to let her go.
What, he's never thought of this before now? Fucking dogshit, he brought it up before. He knows for a fact this is an issue but pursues the relationship anyway because he loves her that much. Plus those lines he gives to her just hurt his character more, as I think it would be more likely he wouldn't say anything at all and she'd have to kinda dig into him a little bit in order to discover his insecurities.
Also that other teacher is a prick and I find it unlikely he realized this based on the information he was given.
Bad author, you should know better than to do this!
That said, this will probably lead to him starving himself because of his family's poverty. Congrats, asshole, you just ruined this kid's relationship and only reliable means of taking care of himself. When the investigation into the child neglect and why a teenage boy is found half-dead from malnutrition, I hope you're ready to explain it's because you were jealous of his relationship with his teacher.