How does Shaw know the Engineers hate humans?

So, at the beginning of the movie, we have the scene where Shaw discovers yet another cave with drawings, all pointing to star charts, pointing out there must be some kind of off world connection between all of their highly unlikely connected groups of people.

Her third or fourth line in the entire movie is:

I think they want us to come find them.

This is entirely based off her own personality and nonscientific bases. (Played off however, on the idea she's a scientific authority. because she was digging in rocks in the middle of no-where with a team)

Our next scene with Shaw comes from David being a creeper and watching her dreams as a child, talking about life and death, and the belief of God and higher planes, Shaw is constantly seen wearing her cross through out the film.

Our next speaking role with Shaw is during the briefing scene...Here it is explained the tall beings pointing to the star clusters drawn between each civilization must be aliens that came to earth....here they conjecture, through scanning and mathemagics, this system does exist, with a single planet with a moon, blah blah blah.

Thats Mr. Dr. Scientist Mans explanation....

Shaws lines, after being questioned by the cannon fodder are:

No, no, not a map, an invitation.

...

They engineered us.

...

I don't, but it's what I choose to believe.

Considering her religious background and her, based on pure belief, assumption that 'God loves us all' the Engineers being the obvious God/Creator reference within the movie...it's unsurprising she sees an invitation.

The rest of the film goes on, then we get to your scene. As pointed out earlier, she hasn't exactly had the best of days...

So our religious main character who thought God created us with good intent, has her b/f killed, gives a 'virgin birth' to a monster (she can't get pregnant normally) all because of the Engineers and their black goo..

She in her world view, can really only come to the conclusion, they must hate her.

She doesn't know they do, but she believes they do.

Very simply put, "why do they hate us?" is an assumption/claim, not a statement of fact. Shaw feels that being put in the position she is must mean that those who put her in that position hate her, because otherwise they wouldn't have put her in that position.

For example:

A - I have a severe case of arachnophobia.
B - I already promised C that you were going to handle that spider problem for him.
A - Why do you hate me?

This is usually said in a somewhat comical way. A is not saying that they know for a fact that B hates them. You're not supposed to take A's question literally, but rather as a roundabout way of saying "I really dislike that you're putting me through this, it's almost as if you hate me and want me to suffer".

Based on the statement alone, there are many degrees of possible interpretations to Shaw's assumption:

• It's comical. She doesn't actually think they hate them; she's just complaining about the situation.
• It's a genuine question, wondering if they were put in the current situation intentionally.
• It's an accusation of intentionally being mistreated.
• It's misdirected anger. The engineers did not intend for this to happen, it happened for unrelated reasons.

In other words, the premise of your question, your inference that her statement means that she knows for a fact that the engineers hate them, is simply not correct.