The reason is simple (credits to FM Dr. Hauke Reddmann pointing it out in a comment):
You are down a pawn without compensation!
Black took a pawn that you won't get back after 6.Qf3 and you don't even quickly get a strong center in return, as you would in some other variations of the QGA and the Slav.
Here is some "proof" that it really is because you are a pawn down:
[FEN "rnbqkbnr/2p2ppp/p3p3/1p6/2pP1B2/2N1P3/PPP2PPP/R2QKBNR w KQkq - 1 6"]
Disregarding the best move a4 (which wins a pawn, which is why it is your only on move 6 in your game), this position where I added back your missing c pawn, the move d5 is evaluated with +0.8 and the move Be2 is evaluated with +0.5.
You already commited a mistake in the opening at move 4. After 3. ..a6 you should play 4. cxd4 (as has happened in almost all master games in the db, avoiding the issues you experienced with the pawn).
You didn't appreciate, that 3. ..a6 has some interesting ideas (just like ..c6). If Black had played the more frequent move 3. ..Be7, Bf4 would've been a great move.
However, after 3. ..a6 4. Bf4, White already has to play very precise to even keep equality where you have to find multiple only moves in a row after Black's best response which is not hard to find for Black!
It is logical that you wanted to get the bishop out, before playing d3 to not lock it behind the pawn chain. Even playing 4. d3 is better than getting the bishop out though, because c4 is defended and can be taken back by the bishop.
The only move that keeps equality for White is 6. a4, because it is the only move that wins the pawn back (and it is thematic not only for these variations but also in the Slav, so you should remember it):
If Black doesn't want you to take twice on b5, he can only advance it to b4, after which the Black pawn on c4 is hanging (attacked by the bishop) and cannot be saved.
in the course the teacher said that if you have better pieces activity, then you most likely have a dynamic advantage and, when you have such type of advantage, is generally a good idea to try to exploit fast, using the fact that your pieces are temporarily more "strong" and "powerful". The usual way to exploit such an advantage is to try to get even more activity/square's control with your pieces and make constant threats, possibly with tempos.
Positionally and logically, your moves make a lot of sense: getting the bishop out before closing the pawn chain, getting the Queen out with a tempo.
However, chess is a very concrete game and we don't get away with schematic thinking.
IM Andras Toth would probably phrase it "don't just be a great story teller - if your decisions are not backed by concrete variations, you're not playing chess".
You chose to go for a variation where you sacrificed a pawn for activity (something very concrete), without actually calculating and checking how your initiative works out concretely.
Which weakness exactly will you attack? How exactly are you going to bring the other pieces into the attack? What does the Queen do on f3 exactly (you will need another move to bring it to g3!)?
How many moves do you need to bring your pieces on good attacking positions if you had "free moves" (always considering that your opponent can develop, too!)?
With every move, your relative development advantage gets reduced (4-1, 5-2, 6-3,..).
It seems that you didn't calculate deep enough, but that you hoped that you would get enough activity.
I know that Qf3 takes the f3 square away from my Ng1, but I decided it wouldn't be so bad...
Qf3 isn't much worse than Be2 or Nf3, but consider that you still don't have enough pieces in play to generate a dangerous attack. It is very important to 'bring all the guys to the party'. Your minor pieces have priority, as they're less mobile and less valuable than the queen.
Your queen has multiple ways to get out, however the enemy pawn on c4 restricts you (your bishop can only get out via e2), so you need a good plan for how to get your pieces out quickly.
6. Qf3 is somewhat a one-mover, as after you gain a tempo on the rook, the queen likely needs to move again, costing you another move. You only 'net gain' a tempo if you can move the queen to a good square with another tempo.