user23219: Original position:

After Bh5 (move I think is better because of the threat to the queen if pawn moves):

After Be6 (move recommended by the engine):


user11629: As the engine is telling you, after 

.... Bh5
g4 Bg6
h4 h5 (basically forced to make space for the bishop; h6 is much worse because white will have the option to open your kingside with g5 and mate you (eventually))
g5 Ne8 (or Nh7 which is worse)
Qb5

is a double attack on b7 and d5, which you cannot defend both.
White will simply win a pawn which explains the ca. +1 evaluation.
With 1... Be6 you avoid this whole line.

user21110: Not only do you lose a pawn as previous answers told, but there's a strategic idea behind this too. What characterizes the position you gave is that it has opposite-side castles. On this positions, players try to pawn-storm their opponents and break their opponent's king position. With Bh5 you are giving your opponent the chance to start a pawn storm with tempo, which means you are basically allowing him to make his desired moves "for free" and succeeding easily on his plan.

23219: <p>Original position:
<a href="https://i.stack.imgur.com/rIfDI.png" rel="noreferrer"><img src="https://i.stack.imgur.com/rIfDI.png" alt="enter image description here"></a>
After Bh5 (move I think is better because of the threat to the queen if pawn moves):
<a href="https://i.stack.imgur.com/cTl3a.png" rel="noreferrer"><img src="https://i.stack.imgur.com/cTl3a.png" alt="enter image description here"></a>
After Be6 (move recommended by the engine):
<a href="https://i.stack.imgur.com/VXKSa.png" rel="noreferrer"><img src="https://i.stack.imgur.com/VXKSa.png" alt="enter image description here"></a></p>
 11629: <p>As the engine is telling you, after </p>

<ol>
<li>.... Bh5</li>
<li>g4 Bg6</li>
<li>h4 h5 (basically forced to make space for the bishop; h6 is much worse because white will have the option to open your kingside with g5 and mate you (eventually))</li>
<li>g5 Ne8 (or Nh7 which is worse)</li>
<li>Qb5</li>
</ol>

<p>is a double attack on b7 and d5, which you cannot defend both.</p>

<p>White will simply win a pawn which explains the ca. +1 evaluation.</p>

<p>With 1... Be6 you avoid this whole line.</p>
 21110: <p>Not only do you lose a pawn as previous answers told, but there's a strategic idea behind this too. What characterizes the position you gave is that it has opposite-side castles. On this positions, players try to pawn-storm their opponents and break their opponent's king position. With Bh5 you are giving your opponent the chance to start a pawn storm <strong>with tempo</strong>, which means you are basically allowing him to make his desired moves "for free" and succeeding easily on his plan.</p>
