Han Solo says in A New Hope,
I've flown from one side of this galaxy to the other, and I've seen a lot of strange stuff, but I've never seen anything to make me believe that there's one all-powerful Force controlling everything. 'Cause no mystical energy field controls my destiny. It's all a lot of simple tricks and nonsense.
In Empire Strikes Back,
He's holding a lightsaber, to open the Tauntaun's stomach and sticks Luke into the Tauntaun's abdominal cavity to temporarily keep Luke warm while he sets up the shelter.
In The Force Awakens, he says to Rey,
I used to wonder about that myself. Thought it was a bunch of mumbo-jumbo. A magical power holding together good and evil, the dark side and the light. Crazy thing is... it's true. The Force. The Jedi... All of it... It's all true.
Now going back to the question, why didn't Han Solo ever become a Jedi during the events of the original trilogy? Kidding aside, for Star Wars fans, they wish to hold a lightsaber more than a blaster. In the films it's obvious that he is not a Force-Sensitive. As the quotes above show, in A New Hope he doesn't believe in the Force. And in The Force Awakens, he admits that the Force, the Jedi are all real. Even at that point, he didn't have an interest in becoming a Jedi. Why is that though he admits that the Force and the Jedi were all true, he still did not become a Jedi?