As you might have noticed several days ago, I promised a post about the correct (better more awesomer) way to use the word "however." It's a common misconception that it's a really good idea to use it in place of words like "but" ("Mice love peanut butter; however, they hate cheese," is pretty much the same as saying, "Mice love peanut butter, but they hate cheese.").
People think it makes them sound really smart and sophisticated to use "however" instead of "but" because it's a longer word and has more syllables. I'm guilty of this myself. A lot, actually; I mean, it's really simple and safe and sounds alright. However, you shouldn't really ever start sentences this way. (See what I did there?)
Unfortunately for fans of this use of the word "however" who are also readers of my humble blog, a professor I had several times throughout college and for whom I have a great respect is completely against the "however, they hate cheese" camp. Professor Eric Hayot of the Comparative Literature department of Penn State thinks (I assume) that this is usage is too common and ordinary and, ultimately, uninteresting (also, all the cool grammarians tell us that you shouldn't start sentences this way -- see above). He suggests a less regular but more interesting and fun usage: "However much I wanted to dance, my level of inebriation would not allow it."
An alternative example: "However I tried, I couldn't lift the elephant."
As you can see, this use of the word allows for greater mobility of language and sentences that are great fun.
If you MUST write a sentence in which you are offering contention of a previous point ("Lions are cool; however, aardvarks are cooler") try to use something a little more sophisticated, such as "nevertheless" or "even so."
And don't ever try to compare lions and aardvarks. Aardvarks will win every time.