When should I not use my front brake?
This comes under the category of things taught to children which simplify the whole truth in order to facilitate learning and keep them safe. Late on they will be ready to learn how to use the front brake effectively.

When children are learning to ride, they are learning lots of new skills. Balance, pedalling and braking. They don't need to apply a lot of braking force as generally they are travelling slowly - whilst still learning - and also have lower mass - than most adults. So, for safety's sake and to simplify the learning they are taught to apply rear brake first, and front brake later to reduce the likelihood of going over the handlebars. In the conditions children are learning in - generally not wet slippy roads - the risk of skidding or fishtailing from applying the rear brake first is lower than the risk of going over the handlebars and the consequences are likely to be lower impact.

Once you have learnt the balance and pedalling and can ride the bike reasonably well. You can move on to more advanced skills to become a really competent rider. One of those is how to stop more quickly when going at speed and with more weight on the bike (i.e. you're bigger). Now the risk of skidding the rear brake, or just not stopping in time due to inadequate braking force applied for the speed and mass is greater and needs to be dealt with. If the front-brake is used properly it can apply much greater braking force, without the risk of skidding associated with the rear brake. The most critical things is to ensure you keep your weight behind the front wheel and not over the top when applying the front-brake. To do this, ensure your weight is toward the back of the bike and that your arms are braced against the handlebars to absorb the force and keep you on the bike.