I've generally found that these arguments can never be "won". People who don't want to learn won't listen, so there's no use wasting your time and effort.
That said, neither one of you are completely right, and both of you are showing your young ages in that exchange. A few points:
-Having a large parrot is like having a toddler: Yes, to a large extent. You are right in that there are many similarities. I joke about it all the time. But there are also a lot of differences, and your friend is right about that. You aren't out of line saying there are a lot of similarities to *only the toddler stage* of raising humans. Other issues arise in human children as they age that are not comparable to parrots, so the comparison stops short.
-The "which is more difficult" argument is so subjective, it's simply not worth having. However, my perspective is this: human toddlers are hands down more difficult than parrots, however, the period of time in which they are more difficult is shorter. She is right about your ability to leave the bird in a cage and go to school or the store or wherever. You can't do that with a toddler (though trust me, there were times when my kids were little that I desperately wished that was possible). You can't call the doctor's office and board a toddler for a few days if you need to. But she's wrong in that there is still a substantial responsibility for the animal's welfare.
-Neither one of you really know what it's like to have kids. You babysit and your friend has much younger siblings. Your friend has more of an insight than you do, but she still doesn't quite know. I also thought I know all there was to know because my parents had another baby when I was a teenager. I was wrong. Your friend is wrong too. What she's missing is something that you do know a thing or two about, and that's the financial responsibility part of things. You also have experience with the reality of not having any back up. If something goes wrong with your friends' siblings, her parents are ultimately in charge. If something bad happens to Lincoln, it's all on you. That's a much heavier weight than just caring for younger siblings a lot.
When it comes down to it, both of you have life experiences that will serve you well. You've taken on responsibility for a parrot and she's in a position where she takes on a substantial amount of care for younger siblings. Both of those things will teach both of you life skills that will serve you well.