Alright, let's see...
The Hippogriff seems to have records of stealth, and great speed...it also seems to have good head-chopping skills. What would you say these would come in handy for? Definitely not a healer...but those head-chopping skills might be useful as a surgeon...hmmm..
Maaaybe an Auror? Stealth is a good thing...speed is a contributing factor...and head-chopping skills are sometimes required. But what if they need the criminal alive?
Meh, as they say, better dead than alive, eh?
For this, let's put ourselves into the shoes (or hooves?) of a Hippogriff. If I were a Hippogriff, what subject would I like...?
History, charms, and any other in-classroom subjects are out. A Hippogriff is a free-spirited creature. Either Care of Magical Creatures or Flying could be possible.
But, uh, Hippogriffs are not really the caring type. They'd probably pulverize the smaller animals...and besides, a Hippogriff has wings, so it doesn't even need a broom! So we're going to go with Flying.
Now we come to the most important part - sorting. We're going to temporarily take over the job of the Sorting Hat, minus the song and stuff.
First off, let's look at its most standing-out traits. Hippogriffs are super proud and distrusting when they first meet you. Only when you prove your trust to them do they become really protective and defensive of you. They're also very very loyal.
Up till now, Hippogriffs sound like a mix between both Gryffindor and Slytherin, but there's also the fact that they focus on what's happening right now instead of what's going to happen in the future.
So Gryffindor it is, pals! Welcome, welcome, to the best house Griffy!
For this, we really need to put in some work. A Hippogriff is distrusting at first, but warms up soon enough. That sounds a lot like a Scorpio. But Scorpios are people who think through things (most of the time, anyways).
But what about Leo? Leo's symbol is the Lion, proud, powerful and incredibly impressive. And, uh, it's a bad idea to insult a Leo, and an even worse idea to insult a Hippogriff...