He's not entirely incorrect.
A strong stripping agent doesn't have a dissimilar impact to fairy liquid. Both rely on harsher cleaning using a hydrophobic reaction.
Ideally you would use a pre clean but if I'm stuck I use fairy liquid and just make sure to wash with a pH neutral shampoo and rinse well after to ensure there's a residue free surface for the wax to bond to.
Yep I agree with Luke, if you want to strip off previous fillers, glazes, wax etc you ideally want a wax remover or IPA but if you don't have any fairy liquid works, and other detailers will agree.
To apply wax you just need to ensure the car is clean from dirt, you can layer them onto of each other.
Polishing, glazes etc are extra steps to either remove or fill in scratches.