This is the last I'll say about Dany because I don't like defending her, but someone has tom
She grew up an orphan with a very abusive brother. Her parents and almost entire family was massacred by an usurper. When she was a teenager, she was sold by said brother into an arranged marriage with a barbarian who raped her. Then she got pregnant and lost her child and her husband.
Keep in mind that some of the people she executed were fighting on the side that butchered her parents, and that ordered an assasination attempt on her own life. Her enemies were allied with people who tried to eradicate her entire bloodline, as she perceives it.
Contrast this with Jon. Although he was a bastard, Ned raised him well, in a safe environment, amongst siblings that accepted him as one of their own, more or less. When he got to Castle Black, he was Mr. entitled I am better than everyone. He was lucky to be surrounded with wise counselors and true friends that gave him sincere advice.
Dany never had that benefit, she was always surrounded by people with ulterior motives who tried to take advantage of her in one way or another. Whether it's the scheming Illyrio Mopatis and Varys, or her husband in Qarth, or thirsty Jorah. She's always had to rely on her inner voice to make big decisions. And she made some bad ones, but also liberated thousands of people. Missandei and Grey Worm probably have a different view of her than some others.
So all in all, she is more of a conflicted, morally gray character than Jon, and that makes her more interesting imo. Compound that with her being hot, and girl power, and I can see why a lot of viewers root for her, despite her shortcomings.
