[ostudent]

for a problem I'm solving, the answer key says that "since the starting material is chiral, each diastereomer is obtained as a single enantiomer"

I would like to understand this better. If I have a chiral starting material and observe diastereomeric products, why would i only observe single enantiomers of each rather than racemates?

Is this because optical activity does not arise spontaneously?

Thank you so much for reading through this.

[PdG3Precatalyst]

It strictly depends on the type of reaction but in many cases the existence of a chiral center causes asymmetric induction. I mean that the reaction occurs stereoselectively and affords mostly one enantiomer because starting material is asymmetric. You can obtain more information from Wiki article
https://en.wikipedia.org/wiki/Asymmetric_induction
 

[kriggy]

This is quite complicated question but basicaly the chiral center might block one side of the molecule so that the other reagent cant acces that side and have to react preferentialy on the other side.
see
https://en.wikipedia.org/wiki/Chiral_auxiliary#Oxazolidinones
as in the "alkylation" scheme you can see that after the enolate formation, the Li⁺ coordinates to the oxygen atoms and locks the molecule so it cant move and the iPr group of the chiral auxiliary blocks the top side of the molecule therefore BnBr can acces it only from the other side.
Evans auxiliary is one of the strongest chiral directors and quite often give very high ee%.

However, in different cases the selectivity might be very low, especialy if the reaction center is  further away from the chiral centre, so you might get product that cant be anywhere between "racemic" (one chiral center is set so its not really racemic but you get 50/50 ratio on the newly formed chiral center) and enantiopure