I can't say whether you should or shouldn't get a pup because I really don't know anything about your lifestyle, but I think your boyfriend has very valid points.
Yorkies can be hard to house train. The pup will likely go all over the carpet at first (and in some cases, even as adults they still prefer the carpet to grass
). It isn't uncommon for carpet to need replacing.
Animal friendly housing can be hard to find. Sometimes rehoming is necessary due to unforseen circumstances, but it wouldn't be fair to the dog to get it knowing that you may not be able to keep it. So it's important to make sure housing will be available before getting the pup. It is a 12-15 (and sometimes even 18) year commitment.
A lot of Yorkies just love to bark and neighbors get upset easily. Getting kicked out for noise wouldn't be unheard of, so depending on the dog, quite a bit of no bark training may be needed.
You said something about maybe having kids someday. Since Yorkies are so small and somewhat fragile, they have to be watched around young kids at all times. Some also don't tolerate kids well.
We usually set aside about $75 a month for Ellie. That is for routine care and a couple things she needs for health issues. For the last little bit, another $50 was added on for a certain drug. I groom her myself or that would be more money. She gets homecooked food, so I don't know exactly how much we spend, but probably between $12-$28 a month. This doesn't include dentals, her spay, emergencies, anything beyond a mild ear infection or something...
I don't want to talk you out of getting one because they are really awesome to own, but they aren't right for everyone.