It seems like there are a lot of convoluted answers to a pretty basic question. The depths for Open Water, Advanced and Deep Diver (all Recreational dives) are recommendations from the agencies. There is reasoning and some logic (and idiot proofing) behind the recommendations.
New divers have been given a ton of new information, and many unfamiliar new skills to perform. The idea is to keep it simple and minimize task loading until muscle memory and a strong knowledge base is built.
It is also a 3 step process to encourage continued education, more diving and experience before going deeper.
New Open Water Adult Diver: 60' NDL for first dive @ 60' is 55 minutes. Gas Time Remaining will control the dive for most new divers. New divers will become low on air before they get too close to the NDL.
For comparison, first dive @ 70' has an NDL of 40 minutes. Most likely, the NDL will control the dive.
Advanced or more experienced Adult Diver: 100' Divers should have enough awareness to plan and perform dives with NDLs and Gas Time Remaining and Time to Surface with Stops, in mind. More to think about and to be aware of.
Deep Diver Specialty: 130' As divers go deeper than 100' and begin to feel some effects of narcosis, they should have some training and experience with recognizing and working through those effects. They should plan their bottom time with awareness of NDLs, plan and manage gas, time to surface and stops.
These are all simple recommendations.
Instructors have strict standards for depth when teaching courses, and those standards can differ from the recommendations above.