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!

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.

OK

The reason for Be2 is simple.  You do not want to play f3 too soon.  Do it when provoked by ...Re8.  Otherwise, there could be Ne4 and Bh4 tricks looming (or Qh4 if the Bishop moves).  Not saying concrete threat here, but the concept makes an early f3 without the Bishops developed risky.

Therefore, where does White want his GOOD Bishop, assuming f3 will get played eventually?  Well, with f3, your good bishop is the dark squared one.  It wants to go to e3.

Without f3 played and without Be2 played, Be3 gets harassed by ...Ng4.

Therefore, White plays Be2 to stop Ng4, then Be3, Qd2, and O-O-O, pausing to play f3 when provoked and not until then.

As mentioned earlier though, Bf4 is the strongest.  The e3-response for the Bishop is on the basis that you are playing the slower strategy with Be2.

I have an ongoing correspondence game at ICCF with 6.Bf4.

We are 25 moves in and the position is fairly equal, maybe a tiny edge for me (white).

Because it's what the engine they use says to do