Maybe if you went through life without thinking that your right you won't have any trouble discussing politics without offending anyone.
Ultimatley though, some people are just not capable of accepting another persons opinion if it differs to their own, and by accepting i mean allowing that person to have it, it is generally these people that have trouble discussing politics with friends and family.
No, that's not the issue. People are entitled to their own opinions. They're not entitled to their own facts.
What I regularly see are people (friends/family) who hold very strong opinions but those opinions are based on emotional need rather than facts. They are pre-disposed to believe a certain way and get angry if there is data presented that contradicts their opinion.
If someone in a discussion says that we've killed 3 million civilians in Iraq, it's not about me simply accepting their "opinion". If someone says that the rich don't pay any taxes my disagreeing with them or saying something is not abotu me thinking I'm "right" about my opinions. If someone tells me that it's a "fact" that we could switch over to wind and solar power in 10 years as our primary source of energy but can't because "big oil" won't let us, it's not about me being "accepting" or open minded.
I don't go looking to debate politics with people who I know aren't that up on the issues. But at the same time, if they're going to start proclaiming their opinions, loudly, in my presence, I have a hard time not gently correcting their misconceptions.