Did Shakespeare write Hamlet because of his son?

I don't think it depicts Shakespeare's relationship with his son Hamnet, rather I believe my Lit teacher said that Shakespeare wrote Hamlet in the wake of his son's death, and maybe that's why Hamlet the play is considered one of the greatest tragedies. Shakespeare probably wrote the play as an outlet for his grief.

Shakespeare Son

Hamnet Shakespeare

"There are several theories on the relationship, if any, between Hamnet and his father's later play Hamlet. Other theories postulate connections between Hamnet's death and the writing of King John, Romeo and Juliet, Julius Caesar, and Twelfth Night, among others. Such biographical theories connecting Hamnet to his father's work began to be popular as early as the 18th century and continued into the 1930s before being dismissed on the arrival of prominent, anti-biographical literary movements such as modernism and New Criticism. More recently, as New Criticism has lost favor among academics, theories surrounding Hamnet and his father's work have resurfaced."

Shakespeare based Hamlet on a Danish legend about Amleth.

Like it says above, Hamlet is based on old old folk tale. So yes, maybe he wanted to do a father/son story because he was a father....but the story itself couldn't have come from Shakespeare's life.