The reason is simple. In a Humanist ceremony, you are marrying not in the presence of god or the state, you're marrying in the presence of your family and friends, so we think it's important that they get to see how you feel, and that makes a huge difference.
Because of the angle at which you stand, the guests can see you, but you can't see them. And I can promise you that in all the weddings I've conducted, I've rarely seen the bride or groom look at anyone apart from one another during the course of the whole ceremony.
It's conventional for the bride's immediate family to sit on the left hand side and the groom's on the right. Nowadays most couples want their guests to mix from the start, so the phrase 'take a seat, not a side' is one to tell your ushers to use.
As to where YOU stand, I generally suggest that the bride goes to my left, diagonally opposite her family. That way they get the best view. The groom usually stands on my right, for the same reason, but like everything else, it's really up to you, so give it a bit of thought.
The bridesmaids and best man or groom's men should also generally stand to either side of you, forming a shallow semi-circle. Again it allows the guests to see them all, and it completes the circle of love in which they and you are joined.