Had a question about counting in japanese from a student's parent the other night so I did some research.
We count as follows, but this family, who lived in japan for awhile, learned as you see in bold:
There are two plausible theories I've read for this:
shi, and shichi are from Chinese. This makes sense; Korean also has its own numbering system but uses the chinese for many situations. Nihongo resources has an in depth explanation. You'll notice the japanese system has yotsu and nanatsu, which were imported into the chinese system. This doesn't explain why, however.
shi has the connotation of death, so the other pronounciations are preferred to ward off bad mojo. I can't find the original pages I was looking at, but Japanese 101 provides some evidence of this, along with kanji.