how is there no centre of symmetry in this case?
One way to quickly get a visualization without building a 3D model (having a model is more instructive, though):


Go to https://chemapps.stolaf.edu/jmol/jsmol/simple.htm
Click on Load by name and type "(2S,3S)-Butane-2,3-diol"
Click on console and type "rotate branch @2 @4 180" to get a conformation that is easy to compare with the Fisher projection.