Our question this week continues the theme of rules that teachers make up to help young students write correctly. The answer is yes, you can start a sentence with however.
Once you start your sentence with however, however, you must make a decision about comma use. If the word however is used as a transition word, you use a comma after it.
The chef prepared the fish exquisitely. However, the service at the restaurant was terrible.
If it is used to mean “in whatever way,” you do not put a comma after it.
However you look at it, you win.
The reason teachers advise students not to start a sentence with however is that by doing so you often lose an opportunity to emphasize part of the sentence. In the first example above, I could have emphasized the contrast between the cooking and the service by placing however later in the sentence between two commas like this:
The chef prepared the fish exquisitely. The restaurant’s service, however, was terrible.
So go ahead. Start sentences with however. But consider whether you could get more mileage out of it by placing it after the specific idea you are contrasting.