> And then you end up with explanations like "Gravity is like a deformation of a rubber sheet".

If you haven't read Eistein's "Relativity : the Special and General Theory", I strongly recommend you do.

It's a book aimed at laypeople, that requires only a basic (1st undergrad semester) understanding of calculus and vectors (not vector calculus, not linear algebra, just vectors). Yet, it's precise and correct, sacrificing conciseness to get easiness to understand - like every teaching book should.

So, no. It's perfectly possible to explain it without the bad analogies.