Ehm? I don't get your "logic"? Qatar is not even neighboring the European continent, nor does it have any cultural, socio- or political connection to it either. Israel has a decades long history with ESC and has been a consistent participant unlike many others since their debut, it already competes as official part of Europe in different international events. Armenia is a former Soviet Republic, Indo-European people belonging to the Europen sphere and also takes part as Europe in different events similar to the fashion of Israel. Armenia is also close to having a 10 year old history with ESC aswell.
Qatar though? What is their connection to ESC and Europe that can be compared to the likes of Israel and Armenia? Absolutely NONE if you'd ask me.
If Qatar is seriously up for discussion then why not as well open threads for Vietnam, India, or Chile etc.? Qatar is about just as much european as them.
Seriously...think twice before opening threads like this.