Why did Miranda have such empathy for the men in the ship in The Tempest?

Miranda is a very open and loving person.  She seems to be caring and empathetic toward everyone immediately.  She also has not met many people, and as soon as she meets people she is very excited.  She is thrilled when she first sees Ferdinand.  She is also very excited to see all of the other men when she sees them in person.

When Miranda learns of the storm, she feels sad.  There has been a wild storm, which was caused by Ariel and her father.  This is an island with a lot of magic users.  Miranda is used to that.  Miranda feels sorry for the ships' occupants and what they might be going through, because Miranda never wants to see anyone suffering.  She asks her father to stop the storm.

MIRANDA

If by your art, my dearest father, you have
Put the wild waters in this roar, allay them.
... O, I have suffered
With those that I saw suffer: a brave vessel,
Who had, no doubt, some noble creature in her,
Dash'd all to pieces. (Act 1, Scene 2) 

Miranda cares about people, possibly because she has no one around.  She has had few examples of people.  Her father is a very interesting person, himself a mixture of compassion and revenge.  Caliban is also a mix of contradictions.  At first he and Miranda got along.  She taught him language and other cultural elements, but then he tried to take advantage of her and now they hate each other. 

When Miranda first sees Ferdinand, she doesn’t believe he is real.  She is entranced by his beauty.

MIRANDA

What is't? a spirit?
Lord, how it looks about! Believe me, sir,
It carries a brave form. But 'tis a spirit. (Act 1, Scene 2)

She falls in love with Ferdinand really fast, because she is of the right age to fall in love and her prospects on a deserted island are pretty low.  She seems to think he is quite attractive.  He is noble, after all, at least he would be if his father remained king. 

When the other people come to the island, Miranda utters her famous line, demonstrating how enthralled she is with all of the men she is seeing (though she has no idea of the role most of the them have played in tormenting her father).

MIRANDA

O, wonder!
How many goodly creatures are there here!
How beauteous mankind is! O brave new world,
That has such people in't! (Act 5, Scene 1) 

Miranda just knows that these people have been shipwrecked and here they are.  At least, we can assume that this is what she knows.  Ferdinand must have told her something by now.  Miranda has a big heart and a sweet nature.  She takes a childlike joy in people and experiences, and wants to see the best in others.