The first and most obvious answer is that the U.S. has formed an Arab coalition that includes enemies of Israel, and those countries don't want the Jewish state to be seen fighting alongside them.
Second, the image of Israel projected in the Arab world portrays it as an enemy unworthy of existence. The Arab world would be reluctant to support any effort that Israel joined because any country that wanted to see the demise of the Jewish state would automatically consider Israel's enemies as friends. That would give ISIS a credibility in those countries that it obviously does not deserve.
Finally, Israel has just gone through a brutal war against Hamas in Gaza that depleted its weaponry after the U.S. refused to rearm the country, leaving its arsenal empty.
Israel is a geographically small country with limited airfields and resources. For it to engage in a war against an opponent that does not threaten its existence, as does Hezbollah, Hamas or Iran, makes neither political or military sense.