Was beer conceived to be a bitter drink? In all the years of my life (except when I was a minor), I've never tasted beer that's not bitter. So was beer conceived to be a bitter drink? What factors in the bitter taste of beer?
So I'm going to assume you mean historically...

The Wikipedia page has a ton of good info but basically, beer was originally a very sweet beverage due to the wild yeast and under modified malt that was used in the brewing process.  To combat the sweetness, brewers would use Gruit which is an herb mixture to bitter the beer. Hops were also used as a bittering agent, but not to the same extent as gruit.

In 1842, the first Pilsner was brewed, a style which showcases hops and is very pale in color which was revolutionary at the time.  This style took Europe by storm and the migrating Germans to the US brought this taste for hoppy pilsners with them to the US.  There were many competing styles that were popular in the US up until Prohibition.
 After prohibition, the breweries that were still in business chose to produce the beers that appeal to the widest consumer base, I.E. Pilsner drinkers. This is the raison d'etre for the very large breweries.

As for the bitterness in beer, the most common factor is Hops.  Hops contain different acids (Alpha, Beta, Myrcente, etc) that bitter beer in different ways.  The type, quantity and usage of hops in the brewing process can affect the bitterness of beer.
That being said, some styles don't use a lot of hops if at all.  Scottish/Irish ales, for instance, don't have much hop flavor due to the lack of availability of hops in the region.  Other styles originate from locations that have never seen hops.

Hope this helps.  Never be afraid to try new things.