Learn English – Reasons for OR reasons that

There are a number of options. Here are the main ones, ordered more or less by frequency of use.

1. Let's talk about the reason you want him to fail.

This is usually equivalent to "Let's talk about why you want him to fail." Note that in this sentence, it's more common to use "reason" in the singular.

@fixer1234 points out a secondary meaning in the comments: parsing "reason" as the direct object of "fail". (To "fail" something is to cause it not to pass.) It would work analogously to this sentence:

Let's talk about the student you want him to fail.
_{e.g. a principal wants him (the student's teacher) to make the student fail.}

But I would say this misreading is very unlikely for "reason", at least without a great deal of context to explain how a person can cause a reason to fail. So don't let this stop you from using this wording!

2. Let's talk about the reason(s) why you want him to fail.

This is equivalent to "Let's talk about why you want him to fail" and is very idiomatic.

3. Let's talk about the reason(s) for which you want him to fail.

This is a little more formal. It certainly can mean the same as the above two.

However, there's another interpretation. The speaker could very well be asking about the reasons for the failure, not for the wanting. That is, "I know you want him to fail. Now, what reasons do you want to cite for his failing?"

This is quite a likely reading, maybe 50/50 with the intended meaning, so I would be careful with it.

4. Let's talk about the reason(s) that you want him to fail.

This is about the same as (1), including the unlikely second reading, except that the version with "that" is used less frequently in everyday speech.