One first impression we get of Sebastian when we first meet him in Ac 2, Scene 1 is that he is in a very gloomy, very depressed state of mind. One might even think he is being overly cynical. His first speech tells us he is feeling very gloomy. Here, he even tells the sea captain Antonio who has just rescued him to stay away from him because he feels he is being cursed by ill-fate and would not want to repay Antonio's kindness by passing his own bad luck onto Antonio, as we see in Sebastian's lines:
My stars shine darkly over me: the malignancy of my fate might perhaps distemper yours; therefore I shall crave of you your leave that I may bear my evils alone: it were a bad recompense for your love, to lay any of them on you. (II.i.3-7)
However, we next learn the reason for his gloominess, which is that he is mourning the loss of his twin sister. His next speeches demonstrate just how much he cared for his sister; he even comments on her beauty, especially the beauty of her mind. He even goes so far as to say that he wishes he had died with her within an hour, just like they had been born together within an hour, showing us how profound his grief over her loss is, which also shows us that Sebastian is a very sensitive character with strong, deep-feeling emotions.