Well, it makes some sense if the Houthis did this cos when they threatened attacks on the UAE in 2020 the UAE did start to withdraw and then, when more threats were made, fully withdrew. They've also spent a lot of money on buying air defense systems (like from Israel) and developing their own.
So they're genuinely scared of Houthi attacks and attacking them or threatening to has proven a good detterent. It may even serve to make them fully give up on their machinations in the Gulf of Aden like supporting the
Southern Transitional Council and maintaining bases in places like Yemen, Socotra, the Bab al-Mandeb and Berbera.
The UAE lives on tourism and trade nowadays (not oil) and thus their lifeblood is the security they promise ajanabis staying and trading here. The second that security begins to breakdown and the UAE sounds like just another Middle-Eastern bombing site it could mean curtains for these saaxiibs' economy.