So, I don’t think that the situation is this black and white. Emotions are very complex and have many layers to them; with that said, you can love multiple people at once, but that doesn’t mean you can’t love the others equally as much. Love is basically endless and has no limits, so I thoroughly disagree with this statement.
Where the issue lies is in the morality of the situation, because if you believe you have romantic feelings towards this girl, then it’s unfair to string your boyfriend along if he’s strictly monogamous. I don’t believe it’s fair for somebody to have to wait for their S/O to figure out their feelings. I’m sure it could leave a massive negative mental impact.
The solution? Communication. Have a discussion with your significant other and explain your feelings to him, and make sure to give him the option to end things if he’s uncomfortable. I also think it’s important to have a discussion with the girl you think you have romantic feelings for, understand her feelings and genuinely talk about the nature of your relationship and where you see it going.
Communication is key in any relationship.