Hello,
Is it a good idea if I should switch to bassoon after five years of playing clarinet would be a suggestion.
I know is that bassoon plays on bass clef and rarely tenor. Fingerings and embouchure is different.

For some reason, my band instructor does not think switching to double reed is a good idea.
Is the bassoon really that hard to begin with?

If you want to give the bassoon a try go ahead. As you say it is quite different to clarinet but many people manage both without problem. However, initially you might have trouble swapping between the two but doing regular practice on both will help here.
One thought is that the BD just doesn't want to lose you from the clarinet section.

I don't really recommend it, the bassoon is a pretty hard instrument to switch to.

You might as well give bassoon a go and then at the end of the day you don't have to carry it on if you find it doesn't suit you - I'm very suprised the BD thinks it best not to take up bassoon - they are usually very keen to gain bassoonists!!