the matrix - Why did Cypher say they were going to kill Neo?

In the beginning of the first movie, in the first conversation, between Cypher and Trinity, he says:

Cypher: We're going to kill him, understand?

Trinity: Morpheus believes he is the One.
Cypher: Do you?

Why did Cypher said that? Was it a habit to kill potential red pills? Was Neo considered to be a threat, so he needed to be killed if he was not the One?

Answer

Instead of interpreting Cypher's statement literally it should be interpreted as "what we are doing has a high risk of resulting in Neo's death".

This is true in general since Neo is older than most people who are unplugged from the Matrix, and Morpheus explains that

We have a rule. We never free a mind once it's reached a certain age. It's dangerous, the mind has trouble letting go.

_{transcript for The Matrix}

The danger posed by an attempt to "free" a mind includes possible death. This is a fact confirmed by the comic Saviors, in which the parents of an adult red pill operative die because they are unplugged from the Matrix and were already too old (H/T @Valorum).

Of course, Trinity knows of this danger and doesn't need to be reminded by Cypher. However, Cypher has two ulterior reasons to say this.

1. Cypher was betraying the crew and covering up his involvement in Neo's likely death as a result of the betrayal.

Here's the dialogue you quoted along with the rest of the conversation:

Cypher: We're going to kill him, understand?

Trinity: Morpheus believes he is the One.

Cypher: Do you?

Trinity: It doesn't matter what I believe.

Cypher: You don't, do you?

Trinity: Did you hear that?

Cypher: Hear what?

Trinity: Are you sure this line is clean?

Cypher: Yeah, of course I'm sure.

Trinity: I better go.

_{transcript for The Matrix}

Cypher was in the process of letting the Agents trace the line between him and Trinity. Later, after Trinity has escaped, the Agents have the following conversation:

Agent Brown: She got out.

Agent Smith: Doesn't matter.

Agent Brown: The informant is real.

Agent Smith: Yes.

Agent Jones: We have the name of their next target.

Agent Brown: The name is Neo.

Agent Smith: We'll need a search running.

Agent Jones: It's already begun.

_{transcript for The Matrix}

The informant is, of course, Cypher. And he has proved to the Agents that he is a true informant.

Cypher expected Neo to die since Cypher did not believe Neo was The One, and Cypher was betraying the crew. Cypher tells Trinity that they're going to kill Neo to raise Trinity's expectations that Neo will not be saved and will die during the process of trying to release him from the Matrix. This will help prevent her from suspecting his betrayal as the cause of Neo's death.

2. Cypher is infatuated with Trinity and attempting to undermine Trinity's belief that Neo is The One.

Cypher repeatedly attempts to convince Trinity that Neo is not The One. If Cypher can convince Trinity that Neo is not The One then, in his mind, she may fall in love with him instead. But as Cypher points out:

I mean, how can he be the One if he's dead?

_{transcript for The Matrix}

Again, if Trinity expects that Neo will die then she will not think he is The One.

Hidden Meanings

There are also two hidden meanings in Cypher's words. Neo symbolically dies twice in The Matrix. The first is when he is unplugged from the Matrix and "reborn" in the real world. The second is when Neo (who is not The One yet) dies at Agent Smith's hands but is resurrected as The One. Cypher obviously does not say that Neo will be killed for these reasons, but his line is for the audience's benefit -- by releasing Neo from the Matrix, they did kill him symbolically (and twice).