Standardization of latent variables in mean-comparison between groups 
Hi!
The above image is from "Latent Variable Models" by Loehlin and Beaujean (p.154).
There are two groups: high stressor group and low stressor group.
The image describes the path diagram for high stressor group but basically its the same for the low stressor group.
The triangle 1 was added to compare the means of the latent variables between two groups.
Accordingly, the paths g and f were set to 0 in the low stressor group while estimated in the high stressor group.
But the part I don't understand is that the two latent variables, D and R were standardized (variance = 1) in the low stressor group, but its variances were estimated in the high stressor group.
I mean why can't I just fix the latent variables' variance to 1 in both groups?
Because 1 in the triangle is a constant, it does not affect the variance of any latent or manifest variable.
Is there any reason that I must fix the latent variables' variances to 1 in the first group but estimate them in the second group?

It's all about model identification.
You don't say, but presumably a-e were constrained to be equal across groups. (Or some of a-e).
If you constrain the variances to be equal, you're making the assumption (which is easily testable) that the variances are equal. If that's not true, your model is wrong.
If you don't constrain either, then the model isn't identified, and it's not possible to fit it.
