Why do the Seventh Day Adventists consider the Sabbath to begin on Friday at sunset? I understand that for the Jews, the beginning of the Sabbath is at 5 PM on Friday. 
So why then does Sabbath start at sundown on Friday for the Seventh Day Adventists?
Seventh Day Adventism is what is known as a restorationist movement. This term is a references to their belief that something fundamental was corrupted or lost in Christianity and that their beliefs have unique insight to restore what was lost to the way it was supposed to me.

In the case of this question, they belief that the vast majority of Christianity from New Testament times on downward erred in their belief that the proper day to worship God changed after the resurrection. Throughout the Old Testament God's people always used the 7th day of the week (Saturday) as described in Genesis as the day set apart for the sabbath. Jews to this day continue that tradition.

Christians on the other hand believe that a change occurred when Christ was raised from the dead that in an senses sanctified that day, which happened to be the 1st day of the week (Sunday). Starting even in the pages of the New Testament you will find believers regularly meeting for worship, prayer, study of the Word, and sacraments on the 1st day of the week. Not a lot of explanation is given, everybody seems to just take it for granted that this was right and proper.

The SDA argument is that even these early Christians erred and that no direct mandate was given that would supersede the creation mandate for the 7th day (Saturday). They believe most of NT Christianity (and the 1900 some years since) was corrupted until their own prophet Ellen G. White set the record straight.

In the case of SDA, they have many beliefs that are different from mainstream Christianity besides just their meeting on the 7th day rather than the 1st. Similar 19th century revelations that "set the record straight" and (in their view) fix corrupted beliefs involve dietary restrictions (also from the Old Testament, discounting the revelations given to Peter about all foods being clean), and not believing in an eternal hell at all.