Chai Nose es Atzmo (Shabbos 94a)

The gemara says that you may be patur for carrying a live person or animal because "chai nose es atzmo" - the person/animal that you're carrying is really partially carrying himself. Tosafos d"h Shehachay asks the obvious question: So what? You're still carrying it! You're chayav for carrying a feather on Shabbos and this is certainly heavier than that. Even if you say that the guy you're carrying is helping you but that's only mesayaya and we just said that you would still be chayav in that case so why should you be patur here? Tosafos answers that the only time you're chayav is if it's similar to a melacha that they did in the mishkan and in the mishkan they never carried live people.

The Pnei Yehoshua points out that this is only true by hotzaa. We see later on the daf that by other melachos even if they're only somewhat similar to what was done in the mishkan (braiding hair compared to building) that you are chayav. However, since by hotzaa it's a melacha gerua (see the first Tosafos in the mesechet) you are only chayav if it's exactly like what they did in the Mishkan.

Someone asked me yesterday morning how you could be patur according to R' Shimon and R' Yehuda for carrying with someone else because that's exactly what they did in the mishkan? They were carrying huge beams and keilim and one person couldn't have possibly carried it by themselves! Tosafos answers this question on daf 3a (d"h Shneihem) that is exactly why they need a pasuk to teach you that you're patur. It's true that without an extra pasuk you would have thought you'd be chayav. Tosafos then asks about other aspects of hotzaa which might not have been done exactly that way in the Mishkan. So you see again that hotzaa is very different from the other 38 melachos. By the other melachos if it's similar to a melacha then it becomes a tolda and is still chayav on Shabbos but by hotzaa because it's a melacha gerua it has to be exactly like they did it in the mishkan.

UPDATE: I saw that the YU Torah online had more:

R. Chaim Brisker (Chiddushim al HaShas) asserts that there are actually two exemptions derived from the same source: Shnayim Sheasauhu, and a “partial melakhah”. Only the first requires that both be capable; the second does not, and “chai nosei et atzmo” comes from that category. (See also Resp. Rabeinu Meshulam Igra, O.C. 8).

R. Moshe Feinstein (Resp. Iggerot Moshe, Y.D. I, 2) explains the position of Tosafot as being that the mishkan only teaches us about a melakhah of hotza’ah in a specific format – where an object will be moved from one domain to the next, and it will be clear from looking at the object in its new location that it was moved by someone. However, with a living being, as that being could have moved on its own power, it is not evident from seeing that being in a new location that someone else did the moving. Using this logic, R. Moshe explains the distinction between an adult and a baby in this realm.
http://www.yutorah.org/daf/