T-Rex might here be going for some rhetorical persuasion, but as logic goes, it's not exactly a sound argument. Even as rhetoric goes, it's the kind of argument that makes you feel like you're getting tricked.
It goes, "I am good at X. If someone else were not good at X, I would do X for them if they wanted my help."
If a friend cleans poop off of your porch, they are doing you a favor. It is not something required of them as a friend, but something they do of their own will simply because they are your friend. The way that you persuade a friend to do a favor for you is usually with an appeal to some kind of reciprocal exchange, which can either be something in the past or the future. You can say, "Remember that time I helped you with that thing? This is your chance to return the favor." Or, you can promise to help out in some way in the future, and this works best if you name something clear and explicit, like, "I will buy you a case of beer." What T-Rex might have to offer in this situation is a promise to clean up vomit for Utahraptor, or something else gross that Utahraptor simply can't deal with.
Your friend is still under no obligation to help you, though, until they accept your offer. They might give Utahraptor's response of, "But I'm STILL not cleaning raccoon poop off your porch."
In any friendship, there is going to be some give and take, and the amount that is appropriate will depend on how close the friendship is, and the amount of reciprocity that occurs. But the bonds of friendship can be stretched if one of the people starts to make unreasonable requests, or is unwilling to comply with requests. People of the latter type, it's still possible to just hang out with them, but people of the former type, we generally just stop talking to.
I do not think that T-Rex's and Utahraptor's friendship is in danger, though. For one thing, Utahraptor is in two of the six panels every single day, and giving him the silent treatment would be kind of difficult. But these ridiculous conversations are almost the bedrock of their friendship. To take them away would be like rain without rainbows.