There may be cultural differences at play here. I will make eye contact with guys but will not hold their gaze for more than a few seconds at a time before looking away momentarily and then re-engaging eye contact again, and so on throughout the conversation. I think it is unnatural to look into someone's eyes continuously, without breaking, while talking. I think it makes people feel uncomfortable. It's like you are staring. It's unnerving for people. It is okay to look away momentarily as long as you re-engage again.
If I need to be emphatic and really press home a point then I will hold his gaze for longer and only break when my point is made. It is a way of communicating your strength of feeling in any given situation. It might be asserting your authority, but equally, if you are comforting/reassuring someone, looking directly into their eyes can emphasise your sincerity - "I really mean this..."
In sex, of course, prolonged eye contact is really important for establishing intimacy with a partner.
In cruising, the normal rules go out the window. Prolonged eye contact, way past the point at which you would probably look away in everyday conversation, is an important way of communicating your sexual interest in another guy. If he reciprocates, you might be onto a good thing. When this happens it carries a huge erotic charge.