But we were told not to...
In response, I told her what I tell people in my writing seminars all the time: it's perfectly acceptable to start sentences with "and", "but", "because", and so on. Indeed, starting sentences with such words is an especially effective way of drawing attention to a contrasting idea or of adding emphasis.
For the most part, rules of grammar we learned as children serve us well in our adult life. But, sometimes the things we were told were rules (and therefore never to be broken) weren't rules at all -- they were more "rules of thumb" designed to avoid more serious problems. Indeed, the "rule" my sister pointed out probably developed because when children started a sentence with one of those words, they usually wrote a sentence fragment (for example: "But I was tired.") and it was easier to set down a rule against starting sentences with such words than to explain what a sentence fragment was to an eight-year-old. (So, another way of looking at it is this: as long as you write a complete sentence, there's no reason you shouldn't start it with one of the forbidden words.)
The wonderful thing about language is that it's dynamic. (If you need proof of this, just consider the difference between Shakespeare's English and today's.) The changes to our language result in the addition of new words (and new meanings to old words) and modification of the so-called rules of grammar.
Perhaps the main justification for taking liberties with some of the rules of grammar we grew up with is that rigid adherence to these rules tends to lead to formal, pompous-sounding writing that is no longer accepted in today's business communications. (If you need an example of the evolution away from overly formal writing consider the (welcome) fact that in modern contracts you won't find phrases like: "the party of the first part" and "the party of the second part".)
So go ahead -- feel free to start your sentences with "and", "but" and "because" if it'll suit your purpose and style. And, if someone tells you you shouldn't do that, just tell them I said you could!