Why do people play the French instead of the Caro-Kann?

it's just a different playstyle... french is more stable, caro kann is more amibitious I would say. There are alot of sharp dynamic lines in the caro-kann that white can choose to go into. In the french black has most of the control over what variation is played, and if black wants to keep things very defensive and stable it's quite easy to do that. For example... I know players who play the rubinstein french, the exchange / advanced, and that's all they need... try doing something exciting against that repertoire. They play for endgames... Not really my style but it works for them. Though this could actually make sense if you just need a draw in some situation. But the caro-kann... you can't do that, white has most of the choice and can take the game into very crazy lines. Like the Tal variation... or the blackmar-diemer transposition. Or the two knights. Or whatever else white likes to play... On the other hand, blacks bishop isnt stuck behind the pawn chain and black exerts more pressure in return as well.
Of course the french player can also play some crazy lines in the winawer, but that's up to them.

French is more solid than Caro-Kann. 1...e6 opens the diagonal of Bf8.
1...c6 obstructs the natural square of Nb8.

As a French player for 29 years, I can tell you both the other replies are wrong.

The French is not more solid than the Caro. The French is actually the more ambitious defense. The closest relative to the French is the Sicilian.

The main difference between the French and the Caro is time versus the Bad Bishop.

Both defenses are light-square defenses, making the c8-bishop the bad Bishop in both cases.

In the Caro, Black's play is very slow, which he does intentionally in order to get the bad Bishop outside the pawn chain, making it bad but active. He takes time to play 1...c6 to stabilize the ...d5 square before pushing ...d5 on move 2. He then proceeds to get the Bishop outside the pawn chain to f5 or g4, before playing ...e6, switching the roles of the pawns, where now e6 will cover d5, and the c-pawn moves again to finally attack White's center. So let's look at this. 1.e4 c6 2.d4 d5 3.e5 Bf5 4.Nf3 e6 and now depending on White's move, it will be at least move 5, and possibly later, before Black attacks White's center, all to get the Bishop out.

In the French, Black goes full-fledged cut throat at White's center. 1.e4 e6 2.d4 d5 3.e5 c5, moving c7-c5 in one goes and already attacking White's center in one go. He will play Nc6 and Qb6, hitting White hard early. The downside is Black's bad bishop is bad and inactive instead of bad but active like in the Caro.

The French is the more aggressive defense. The Caro is the more solid defense, but it takes Black for ever to attack White.

Your post is getting lost in semantics - black having more initiative ultimately means black can play a safer position, and in some cases can turn on the aggression if black wants to do that, but that's not required of black, black is not compromising his position in some way that makes the position fundamentally aggressive. When white can choose one of a dozen attacking variations vs. the caro, compared to the french where he has 4 choices, 2 of which are drawish and the other 2 give most of the power to black, it's pretty clear the french is more stable. And Anish stated in his course on the french that it can be a strong drawing weapon, and it obviously can be, so... if you need a win as black and white just needs a draw you wouldn't give white the opportunity to play an exchange french. However, if white chooses to go into the tarrasch or paulsen certainly black can play it extremely aggressive, at that point your logic works - but black can also play it solid if he wants, like if he just needs a draw - there's another GM forgot his name but he plays the rubinstein in drawing situations, so...

If you want to understand things the best of all - play them both. You'll learn a lot from each of them.

The French has things to teach you that the Caro-Kann won't. And the Caro-Kann has things to teach you that the French won't.

It'll take more effort and time, but if you're up for the challenge - learning from each of them will make you a stronger player than just focusing on one or the other ...

why do i like vanilla ice cream more than chocolate?

Because your taste buds are messed up. Chocolate beats Vanilla 11 times out of every 10!

I consider it a tempo vs. activity question, at least at the most surface level. The Caro loses a tempo compared to the French, since the c pawn moves twice to get to c5 instead of just once, but the French loses activity to the Caro, since the Bishop gets blocked in. Obviously there is way more depth and diversity to the openings than that, but as far as a core difference in the first few moves I think this is noteworthy.