Why would you try to score a goal when it is 4 on 4 in hockey?

Ignoring the real world answer that others have already given, even hypothetically, the premise of this question is shaky. If you assume scoring would put you on the penalty kill, why wouldn't you still want to score?

If you score, your opponents get part of a penalty kill and can either (A) score a goal, evening the goals scored in the situation, or (B) not score a goal, leaving you one up.

If you don't score, your opponents don't get the penalty kill, don't score, and you're still even in goals scored.

In other words, getting a goal and going on the penalty kill either puts you at even or at +1 goals, while no scoring only leaves you even (assuming they don't score at even strength). There is an upside to scoring, but no downside. Why wouldn't you go for it?

It's very rare but if one team has a player in the box then the other gets one seconds later the team that gets scored on gets to have their player back on the ice for the remainder of the other teams penalty. It's still advantageous to want to score on a 4 on 4 then kill the little bit of time remaining on what would turn into short penalty kill for the team that scored.

no, in 4-4 both teams have the same amount of players on the ice. there is no power play, no penalty killing which means nobody would get out of the box on a 4-4 or a 3-3 goal

no nobody would get out of the box in a 4-4 and not even 3-3 wel thats the way i understand it