1. Consider how the person was brought up. Childhood, religion, and general beliefs could be a cause. Some people are brought up with one mindset on a wide variety of topics. If someone says pitbulls are mean, maybe they grew up in a place where the animal wasn't so friendly.
2. Talk in a calm voice. Since a large part of the internet is text-based, nobody can really tell the tone of person behind the screen. "I hate you" can sound playful, mean, or even sarcastic. Unless you're talking to the person in real life (not recommended or encouraged), you won't be able to figure out how their words sound. Use patience and avoid arrogance and stubbornness.
3. Look on the other side. If you were in the person's shoes, how would you feel? You should never say a person's idea is wrong, because yours can be just the same. In the end, you both might be right or wrong.
4. Educate yourself. There's nothing worse than a person explaining their opinion to someone if they don't know about the subject. Vice versa counts also. Know your stuff so you won't be ridiculed.
5. Avoid the person if they insist on declining your idea completely. This is a last resort if they insist that you're the wrong one, and constantly bring you down with their opinions. On the internet, this is called a troll, and their race should be avoided at all times. Anger and nasty comments just feed them, making them grow.
The day I ever decide to give up on anything is the day the internet goes on the endangered species list and humanity starts savaging for WiFi passwords, and that fate is yet to come true.