Major spoiler alert! If you haven't watched the latest episode of Game of Thrones, turn back now.
In the latest episode of Game of Thrones, "The Last of the Starks," we see Daenerys Targaryen pushed to the brink of her limits. She just found out her lover is her nephew and that he has a better claim to the throne. She witnessed the death of Ser Jorah, who was one of her most trusted advisors. Then, she sees the beheading of her best friend and closest confidante, Missandei, but not before losing one of her children, Rhaegal, to Euron Greyjoy's dragon-killing arrows. The last we see of Dany, she is fuming, and radiating with rage. This leads many Game of Thrones fans to wonder: Will Daenerys turn into her father (King Aerys II Targaryen) and become the Mad Queen?
Season 8 is already positioning Daenerys to seem unworthy of the Iron Throne
If the last seven seasons lauded Dany as a natural leader with true potential for the Iron Throne, Season 8 has done nothing but unravel all that she's worked for, and that's a shame. Dany has proven time and time again that she believes in a peaceful realm, one without tyrants, corruption, or slavery. She liberated the slaves in Slaver's Bay, won over the Dothraki, as well as the Unsullied, who all pledge allegiance to her and lovingly accept her as their queen. But as soon as she stepped foot in Westeros, she realized that not everyone would want to bow down to her.
The people of Winterfell are skeptical of her and her dragons, and they don't trust her leadership—after all, it's not like everyone is privy to everything she accomplished beyond Westeros. Plus, people just don't trust Targaryens after what happened with King Aerys—they believe that all Targaryens are susceptible to going mad, due to the family's inbreeding (more on King Aerys later).
Besides the Northerners' distrust of her, the showrunners have practically gone out of their way to portray Daenerys as short-tempered, impulsive, and constantly threatened this season. Case in point, Daenerys completely ignores Sansa's advice to let the soldiers rest and heal before they march into war again, this time with Cersei's well-rounded army and resources. She also basically has a tantrum when Jon tries to convince her that he doesn't want the throne, and tries to convince him to never tell a soul about his parentage, not even his sisters (well, his cousins). The show has pivoted her character so intensely, that even Varys and Tyrion (more so Varys) have started to doubt her mental state and qualifications for leadership. Is this the character trajectory George R.R. Martin planned for Dany? Or is it just lazy writing? Regardless, Dany has lost her cool, and for now, we have to go with it.
Dany's family history points to her inheriting her father's traits
King Aerys II, Daenerys's father, ruled as a benevolent leader until he became increasingly paranoid, and eventually went mad. He hid wildfire throughout King's Landing (some of which we see Cersei use to blow up the Great Sept of Baelor a few seasons ago) and eventually wanted to "burn them all" (aka, all the people in King's Landing). Jaime, who served in King Aerys' Kingsguard, tells Brienne back when they're captured in Season 3, "He burned anyone who was against him. Before long, half the country was against him. Aerys saw traitors everywhere. So he had his pyromancers place caches of wildfire all over the city." Jaime ended up killing him before he could light the city on fire, which earned him the nickname "Kingslayer." Dany has been warned by her council over and over to not repeat her father's mistakes. For the most part, she hasn't gone overboard with her temper or her dragons. But she's also slipped a few times.
For instance, when she burned the Tarlys alive for not bending the knee
Back in Season 7, Dany had her dragons ruthlessly roast Sam's dad and brother for not bending the knee. Could she have maybe let them go with a stern warning instead? Maybe. In Episode 1 of Season 8, when Sam learns about what she did to his family, he understands what she's capable of, and that she'll do just about anything for power and control. (To be fair, she did give them a choice—and they were allies with the Lannisters, after all.)
Other less dramatic moments, such as her flare-ups with Tyrion (she constantly blames him whenever anything goes wrong, nearly firing him as her Hand) and constantly telling her council that it's her "destiny" to sit on the Iron Throne, that wanting to be ruler is all she's ever know or wanted, show that she's not exactly mild-tempered. It does make us wonder: If she were a man, would this behavior seem so alarming?