Why people like Bakugou from MHA?

Well, for a starter he is the most well-written character in the manga. He bullied Deku when he was a kid up to middle school, but he gradually mature. He doesn’t like fellowships, and in his road to becoming a hero, he forgets to consider other people or just because he doesn’t give a fuck.
People also like him for comic relief the author has portrayed.

Horikoshi have brought the reader from this surprise to another. The constant anger, his determination, the aggressive and arrogance that hides a brilliant mind. A fair man who won’t take what he doesn’t own. He more prideful, aggressive and arrogance than anyone else in the series. Even the villains also see his potential but why would he want to become a villain. Bakugou is a boy who has everything: a great quirk, a happy family, and peaceful infancy. He has everything he ever needs. And he believes he will get everything he craves.

The author gives the character so much deep and complexity. With everything he has, Bakugou still suffers from his superiority complex. He has the most significant developed. He matures every day through everybody he met. He might have a look of a gangster, and his anger behavior will give people a wrong expressive. He is at the top of his class, not only in battle but also in studying (even higher than the main character). A fair man who won’t take the medal that he didn’t earn the rightful way.

The kind of coolness his personality portrays on the show, in contrast to Izuku’s sincere, innocent way, really puts things into focus when you notice how different people can be.

The relationship between Bakugou and Deku in My Hero Academia?

To be honest, I can only say they are a mess. These two are a little obsesses with each other from my point of view. We already know that Bakugou aggressive behavior toward everybody, but toward Deku is worst. His bullying behavior from when they were children still have an effect of making Deku a shy, embracement man like he is right now.
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If you read the manga, in later chapters, you’ll see for Bakugou’ belief a hero will always win. That is his definition of a hero. His religion. Seeing Deku, someone he has looked down on his entire life is getting stronger and more powerful hurt his price a lot. He felt betrayed for being foul around. I watched the anime first, and I used to think that he just a side character that will soon be outgrown by the main one but Horikoshi has surprised me in a good way. Bakugou is a prideful and bitter man. He always pays attention to Deku and Todoroki, the two whom he saw as his rival. He is an asshole, but I can make myself hate him. He is my source of comedy in this whole series.
Deku first impression is a timid, shy and forgiven person. I am sorry. I don’t like him at first due to he cried a lot. I wonder if his tear is his superpower. But he has grown tremendously from those days of timid. He is still kind but he stronger now. His faith never changed. He believes that becoming a hero is to save someone. That is his religion. I started to love that broccoli head of him.  Like All Might has stated in the manga that these two are like two sides of the same coin. They all admire All Might, but their views are way different.
I was surprised in the manga too, at first I think only Bakugou obsess with Deku, but I’ve learned that this is a two-way road. If you consider from the first few chapters, you will see that Deku did generally care about Bakugou despite being bullied by him. When Bakugou told Deku to kill himself, Deku has thought that “Idiot! if I really jumped, you’d be charged with bullying me into suicide!! Thinking before you speak”.
Not to mention the epic moment when he runs toward the mug villain. When Bakugou is the target of Ledge of Villain, Deku runs everywhere to find him too. But I think the important detailed here is that when he is in the rescued mission, he sent Kirishima instead because he understands Bakugou. He knows that if it is Kirishima, Bakugou’ pride won’t hurt. (Oh, come on! You have to watch his face before you rescued him). This scene also stated that Deku never actually stop watching Bakugou. He knows what is going on around Bakugou. The flashback from when they were children also showed that Deku was always watching Bakugou from the sideways, and no matter how much Bakugou beat him up, he never stop following Bakugou.
The dynamic between these two is what makes so many people ship them and hate the ship at the same time. Their relationship did get better after they fight in chapter 118. Deku prized Bakugou winter costume and Bakugou point out some problem with Deku technique.