Goodness knows, there are lots of ways that liberals and conservatives manage to annoy each other. Still, one that has struck me recently is an odd sort of bragging rights.
One of the main divisions between these groups at this point in time is over how the less vulnerable in society are best provided with care. The liberal view is generally that comprehensive government programs should be set up to assure that everyone in society has a certain basic level of food, income, medical care, housing, babysitting, rice pudding, etc. The conservative view is generally that guaranteed government handouts create dependency and hurt people in the long run, and that short term help for those in trouble is generally better provided by family, church or private charity.
The problem comes when members of these two groups get together and start arguing about how to help others. At this point, the liberal may say, "I advocate this particular program currently up before congress, which will provide housing, medical care and rice pudding subsidies to at least ten million suffering people who current lack at least one of these things. How can you possibly be against giving these basic needs to people who don't even have rice pudding? To pay for this, we will charge a five dollar tax on every large, ugly pair of shoes best suited to stomping on innocent bunnies that is sold. This will not only help those without rice pudding, but create an incentive for people to stop stomping on innocent bunnies."
What can the conservative reply to this?
He might say, "I really think it's better if people without rice pudding receive temporary help from their families and communities until they're back on their feet. And however one may feel about stomping on innocent bunnies, work boots are generally worn by the lower classes and so the tax you are suggesting is regressive. Many of the people wearing bunny-stomping boots themselves have trouble affording rice pudding."
He might well say that, but in some senses it's an unsatisfying answer. The liberal may rest assured that he is personally doing something both to help those without rice pudding and to remove the means to stomp bunnies, while the conservative is vaguely suggesting that someone-or-other (who may or may not actually step up to the plate) ought to do the helping instead of the government.
In other words, the liberal gets to sound like he is personally doing something about the issue by supporting legislation which will in turn tax everyone and help large numbers of people. The conservative says he supports more local/charitable efforts, but while it's considered polite to talk up the legislation you support, it's not considered polite to brag about recent charitable donations you have made. It may be that the conservative just wrote several large checks to rice pudding-providing charities, and perhaps even takes potentially stompable bunnies into his home, but if he brings this up in conversation, he sounds like a jerk. Plus, no matter how much he's doing at a local level, it can be assured that these local efforts are not helping all ten million children currently without rice pudding who would be helped by nationwide legislation.
This, in turn, makes the conservative growl inside and gnash his teeth, since he knows that he's coming out sounding like he doesn't help anyone (and doesn't want anyone helped). It doesn't help when the liberal then announces something along the lines of, "You conservatives only care about making sure the rich have rice pudding," or "You conservatives care plenty about the unborn, but once they're old enough to eat rice pudding you walk away."
So the conservative thinks that the liberal is a hopeless bragger who doesn't do anything to help the poor himself but is happy to tax others; the liberal thinks the conservative is a heartless skinflint who doesn't lift a finger to help those without rice pudding; and the local rice pudding charities wish that everyone would stop overlooking all the hard work they do just because they don't have the nationwide scale (and confiscatory authority) to help ten million people at a time.