So let's dive into this question to answer it.
None of your options is correct. The right sentence would be:
"Dive right in, [as to] why you're involved"
Let's look at cambridge.org:
The phrasal verb is dive in/dive into something and not dive in to.
You could rephrase your sentence like this:
"Dive right into the question, why you're involved"
Here you use into as you have the something as target for your diving which is "the question". If you omit the something you should change from "into" to "to".
See the examples of to break in/break into something.
- The burglars disabled the alarm and used a glass cutter to break into the house.
- Thieves broke in and stole jewellery worth thousands of pounds.
The first sentence has the target "the house". In sentence two the target is omitted, so break in is used.
From the second sentence we can deduct a reason for the action and here we will finally find the break in to
- Thieves break in to steal jewellery.
- Thieves break into houses to steal jewellery.
For all the people that might say:
The verb is dive in so dive into must be wrong, and camebridge.org is wrong!
let us look at other dictionaries:
- Merriam Webster "to start work on energetically"
- Oxford "Occupy oneself suddenly and enthusiastically with [...]", "dive into a barbecued beef burrito"