why do most masters play be2 in this position?

here it is: https://www.chess.com/explorer?moveList=e4+e5+Nc3+Nf6+Nf3+d6+d4+exd4+Nxd4+Be7+Bc4&ply=10&origMoves=e4+e5+Nc3+Nf6+Nf3+d6+d4+exd4+Nxd4+Be7+Bc4&ne=1

bc4 is better imo

so why do most masters play be2?

because castling long for white leads to a pawn race to get each other's kings, and many players do not want to play that precisely.

im pretty sure that bc4 controls more of the board than be2

Bc4 looks active, but after ...0-0 it doesn't seem like you can exploit the b2-g1 diagonal soon. You might also lose tempo when Black expands on the queenside hitting the Bishop and there are possible forks with ...Nxe4 followed by ...d5. Be2 also controls g4. Why do you think Bc4 is best?

Btw I'd look into g3 (slow) and Bf4 (sharp).

The raw amount of squares is a marginal criterion.

Note that according to ChessBase online, masters prefer g3 (avg ELO 2317) over Bc4 (avg 1946) and Be2 (avg 2098). FWIW.

The most popular move by far after 6.Bc4 0-0 is 7.0-0, so what's your point?

bc4 is an invitation to get hit by a pawn. Be2 doesn't get in the way of anything, prepares kingside castling and then f4 (white may or may not want to play f4)

They wanna go for the Sicillian Classical canna structure with Be3, they go long castle and then push king side pawns and so the 2 bishops are very useful.

I believe many of the previous posts should have answered your question, but I will add a little more. The bishop at c4 can become a target and help black speed up his pawn storm, especially after we castle queenside. For example, after black plays ...a6, ...b5 and ...b4 come with tempo  (because they will attack white's bishop and knight) and the pawns will run very fast. Additionally, our bishop at e2 can support a g4 pawn advance and even stop ...Nh5 when we push g5.

That's a plan, but I don't think White has an advantage then. But you're right: if White goes 0-0-0, the Bishop should go to e2.

6.Bc4 is a principled move, but those principles often does not work well in positions without pawns of opposing colors on e4 and e5. Here the bishop is unstable on c4, prone to harassment from Black's queen's knight and b-pawn. A well-timed ...Nxe4 followed by ...d5 and White loses his central control. In practice White often proceeds with a4 (to stop ...b5) and Ba2, only to see the bishop exchanged after ...Bc8-e6.

6.Be2 is intended to prevent Black counterplay. The bishop will go to f3 (after playing f2-f4 to prevent ...Ne5), where it gives extra protection to e4 and puts pressure on d5. Forget about O-O-O. Dragon-style attacks won't fare well if Black hasn't weakened his kingside with ...g6.

The idea behind 6.g3 is similar to that of 6.Be2.

Thank you for all of your responses!

"Most masters" play either 6.Bf4, or 6.g3 in this position.

6.Bf4 has a quick queenside castling and kingside pawn storm in mind, while 6.g3 takes care of Black's most common idea of an eventual ...c6 and ...d5.

Are you new to chess? The highest theory of chess is full of opposite side castling attacks against non-fianchettoed pawn formations. O-O-O is particularly advantageous against Philidor style openings because black has no semi-open c-file and if he moves his c-pawn his d-pawn can become very weak with no e-pawn. 

Bf4 followed by queenside castle is fine for black, otherwise we’d see an over abundance of players playing this line.

Let's see how masters repel your "advantageous" opposite-side castle attack, often with a more ferocious one against the White king.

The Dragon-style attack, which focuses on pushing the g- and h-pawns, is a bit too slow for the ...exd4 Philidor, as it is in other openings where Black hasn't moved his kingside pawns. It is further proved by the fact that White scores only 49% in the critical line 6.Bf4 O-O 7.Qd2 c6 8.O-O-O b5, according to ChessBase LiveBook. Black does not need a semi-open c-file to conduct a successful attack, and he can afford to lose his d-pawn in most lines.

Such a risky idea would be "advantageous" only at your "new-to-chess" level, where players know little about how to counterattack.

Pardon me?

Some 2,000 games played, and white is scoring quite above average.

Personally I prefer 6.g3, as the mainline after Bf4 is extremely sharp, and I don't want to memorize a ton about a variation I will not meet frequently.

This ...c6 and ...b5 line has been practically archived in correspondence games as bad.

After 9.f3 b4 10.Na4 the only move where Black has not lost all the games is 10...Bd7, which still is scoring a miserable 15% (mainly due to older games, in recent ones he is barely able to survive without devastating material losses). Most recent game, where a correspondence IM went down the drain against a player rated 400+ points lower:

In short, all your claims are quite unfounded.

Like it, or not, 6.Bf4 is white's most agrressive and dangerous line by a wide margin, but there are a couple of lines (not the one which you've suggested which is just bad, and white does not need to know more than leaving the a4 horsie unprotected) where he needs to memorize a lot.