Here's some of the reasons:
"In a web poll taken by 989 respondents, 49% said religious conviction is the main reason they continue homeschooling; 15% positive social environment; 14% academic excellence; 12% specific needs of child; 5% curriculum choice; and 5% flexibility." -- taken from Youcanhomeschool.org
Does it work?
"By grade 8, the average homeschool student performs four grade levels above the national average." -- ibid
Now, let me ask: Given the state of what's happening in the public school sector -- take any area you want: discipline, education, shootings, etc. -- do you really have to ask this question?
Congratulations on the doe! And even bigger kudos for involving your daughter. What a biology lesson!!