Whoever decided that browsers would "do their best" with invalid HTML was responsible for the nightmare of non-validating web pages that we have at the moment.

It may seem anoying sometimes, but regardless of how forgiving browsers may be, people (and machines) will allways be faliable, and will allways make mistakes. Would you prefer it if browsers just refused to show any page with the slightest HTML glitch?

Ultimately, the choice to "do their best with invalid HTML" can be traced back to the defacto mantra of the IETF...

Be liberal in what you accept, and
conservative in what you send.

For more background, consult RFC791, RFC1122, and RFC1958,