There is a beer for everyone.
Someone you know claims to not like beer? You don't like it yourself? Baloney.
I bet you just haven't found a kind of beer you like yet. There are literally thousands of different beers being brewed all around the world. Go into a decent bottle shop and you will literally have hundreds of different beers to choose from. We are in the golden age of craft brewing. Pale, fizzy lager is no longer the only option we're faced with at the beer cooler. If that's all you've ever been exposed to, I envy you. You are in for a great treat. A range of brand new, delicious, diverse flavors awaits your appreciation.
Of course, I'm not going to send you off half-cocked. As with any true appreciation, you should begin with a little forethough:
First, it's very unlikely you're going to have an appreciation for huge amounts of hops right off the bat. Hops are responsible for bitterness, as well as a floral, piney, citrusy flavor and odor. It's unique and sometimes offputting to someone who doesn't like beer. As you develop your palatte, you can begin investigating this unique and truly delicious flavor. For now, stay away from anything called "India Pale Ale (IPA)," "Barley Wine," or "American Strong Ale"
Second, my intent is to have you begin with things you are likely to find easily. Depending on where you live, you might have to go to the hippie supermarket to find a couple things, but they should be available somewhere.
Third, get your beer from a bar or buy yourself a pint glass for drinking at home. If you drink from the bottle or can directly, you're missing out on half the experience. You think ice cream would taste great coming out of a toothpaste tube? Probably not. So pour those beers into a glass and get your nose in there.
Last, you should absolutely view this list only as a starting point. Most of the beers listed below are what you'd call "approachable." They're well made and delicious, but none are really popping with flavor. Once you start to get a feel for the flavors you appreciate, by all means seek out similar brews with richer, more distinct flavors.
The first beer I'm going to recommend is Guinness Stout, simply because it's the antithesis of what most people consider "beer." It's dark, smooth, and rich; a far cry from fizzy and yellow. Approach it more like a glass of chocolate milk than a glass of soda, and you might find yourself falling in love with the roasty, chocolately flavors it's known for. If you can't get it from a nitro tap, be sure to buy it in a can to get the full effect of the dissolved nitrogen.
If rich, dark beer isn't your thing, you might try a New Belgium Mothership Wit. This is a much lighter beer, brewed with wheat malt in a Belgian style. It has strong citrus presence, derived from spices and orange peel. It is effervescent and highly refreshing.
If you're ready for something with a little hop bite, you can't go wrong with Sierra Nevada Pale Ale. This is probably the quintessential West Coast pale ale. It's a perfect blend of crisp malt and citrusy Cascade hops. It's rich without being overpowering or heavy, making it easy to enjoy one after another.