Why did it use "would have" here?

Question

source

Not that I’m saying you’re necessarily an enemy. I mean, I don’t think you would really have shot me.

I looked up "would have".

1. We use would have as the past tense form of will have:
2. We use would have in past conditionals to talk about something that did not happen:

I don't understand why it used "would have". If I make the sentence, I would just say

I don't think you would really shot me.

Answer 1

Education First calls this the type 3 conditional. The source states that this form

is used to refer to a time that is in the past, and a situation that is contrary to reality.

These both apply to your situation because

1. The sentence refers to an action begun and finished in the past (Vanessa pointing the remote at the Doctor).
2. The situation the Doctor refers to did not happen (The Doctor took Vanessa's remote, though it turned out to have no firing capability).

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Now, you mention that you would structure the sentence to say

I don't think you would really shoot me.

In this case, that doesn't work. This is because the Doctor is referencing one particular situation in the past. This sentence doesn't talk about a past situation; instead, it talks about a general hypothetical event. However, it is awkward by itself, with no mention of the event. It would make more sense to say, for example (these are my own additions):

I don't think you would really shoot me if you knew it was me.

I don't think you would really shoot me even if you had a real firearm.

But notice when the tense changes from simple past to past perfect,

I don't think you would have really shot me [if you had known it was me].

I don't think you would have really shot me [even if you had had a real firearm].

the conditional changes into a perfect conditional.

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To summarize, the sentence uses would have because the event referred to is a hypothetical past situation; with your idea, the event is more general.

Answer 2

'Would have shot' is in the conditional perfect tense, which is the correct tense in this case.

The base sentence, showing this tense in the third conditional would be:

If you were my enemy, you would have shot me.

Negating this sentence gives us:

If you are not my enemy, you would not have shot me.

A slightly more complex version of this sentence could be:

If you are not my enemy, I don't think you would have shot me.

In your case the writer has split both parts of the conditional sentence into two separate sentences. This is not usual, but it is allowable. In effect, this now becomes:

I don't think you are my enemy. As a consequence, I don't think you would have shot me.

Add in a few more words for dramatic effect, and you end up with:

Not that I’m saying you’re necessarily an enemy. I mean, I don’t think you would really have shot me.

The use of 'would' in the second sentence shows that this sentence is in the conditional mood. The use of 'have' shows that it is in the perfect (ie past) tense. Removing 'have' would change the sentence structure from conditional perfect to simple conditional, which puts it in the present tense. This would require the verb 'shot' to be replaced by the verb 'shoot'. So your amended sentence would change from:

I don't think you would really shot me.

to

I don't think you would really shoot me.