Yes, you can, by using the Go to page based on answer feature. This implies that you have to divide your form into pages, which is easy to do.
Given you have already created your form with three questions:
- Do you like cats?
- Which kind of cat do you like most?
- Why do you dislike cats?
Create a page for each section of your form:
- Click the Add item button
- Select Page break
- Move question 2 into your new page (drag-and-drop)
- Add a new page break
- Move question 3 into your new page
You should now have three pages; one for each question.
Now make your first question a Multiple choice question, and tick the Go to page based on answer checkbox:
Add options to your question (Yes and No). For each option, select the page to go to if that option is selected:
On page 2 (with the question Which kind of cat do you like most) you would want to skip the next page (Why do you dislike cats):
That's it. I've setup an example form here, feel free to play with it: