The first thing that would've come to my mind was how are you going to play the turn and river if we decide to just call.
There are as a lot of "scare" cards that can come on the turn. (any Q, J, 4, or spade) That is a lot of cards - potentially 15 (assuming villain is holding 2 of the actual 17 cards villain could be holding (2 higher spades, two pair/ set combinations). We want villain to go away now, since our hand is potentially vulnerable.
Still, if we cold call this bet villain may think we have a hand weaker than a flush and come swinging on the turn with a hand weaker than yours, most likely a set type hand. Basically cold calling the flop won't tell us whether we are beat or not and we need to know because there are two more streets to come and villain could easily bet on both of them with a weaker hand than ours.
A raise is best because while villain will usually fold hands weaker than ours, we will find out if he has higher flush if he decides to call/ raise over our raise. There aren't a lot of players who won't lay down 2 pair or a set if you stick in another raise, and i am going to assume that all players would lay those hands down for my equity calculation.
So, Equity wise... (There is $13.50 in the Pot)
If you raise to $15 and villain folds... Probability: 66%
($13.50 x .66) = $8.91
If you raise to $15 and villain calls/ raises... Probability: 33%
(-$6.50 x .33) = -$2.45
Total Equity: $6.46
If you were instead to call villain down to the river, he would show you a higher flush 33% of the time and a full house probably ~11% (since he had 2 streets to potentially pick up one of his 4-6 real outs). We are assuming villain did not have a hand that was still drawing to a higher flush for this calculation.
You call two streets worth of bets (1/2 ($11) and 1/3 pot ($15). We can ignore the flop raise because you would've called it anyways if you were going to raise him there and i eliminated that variable from both equations.
If villain has a higher flush... Probability: 33%
($26 x .33) = -$8.58
If villain has a full house... Probability: 11%
($26 x. 11) = -$2.86
If villain has only a set by the river, he will bet both streets (in this example, but you may be able to get more out of him if he checked and you made a slightly larger value bet). Probability: 55%
($26 x .55) = $14.3
Total Equity: $2.86
Raising on the flop saves you from calling down 2 streets with a worse hand, and you don't compensate enough from weaker hands that go to showdown with you.