I am going to have to respectfully disagree with some of the above posters, based on my own experience. While I understand that the concern for safety is paramount; there is no reason why a reasonably athletic beginner on a well trained school horse can't be trotting over cavaletti and a pile of poles on the ground or a tiny crossrail with 10 lessons.
The advantages of doing so (no, it's not just about advancing students quickly to keep their interest) are to make jumping seem like not such a big deal or a big step up, but just part of everyday riding, and to give them lots and lots of practice with maintaining jump position, eyes focusing up, not interfering with the horse, before the jumps get any bigger or more complicated.
If you don't have a good school horse, stabilized on loose reins, that responds to voice commands, then no, it's a bad idea.
If the beginner is timid or fearful, then it's a a bad idea. If the beginner can't maintain a decent design of position in two point grabbing mane, then it's a bad idea. (Just design, mind you - they're not going to have strength or grip yet.)
But a well taught, reasonably athletic beginner on a stabilized school horse? No reason not to.
I suspect that a lot of you who are upset by the idea come from the teaching philosophy that you should be able to 1.) ride on contact and 2.) sit the canter before jumping. If that's the case, a year or two of instruction is about right to master those to skills. And if the only horse available to teach on is an intermediate level horse that needs to be ridden to a fence sitting and on contact, you're right again - the student shouldn't jump *that horse* until they can do those things.
However, in 20 years of teaching Litteaur based instruction, 75 - 80% of the beginners were trotting poles/crossrails in two point, grabbing mane, in the first ten lessons, with very, very, few falls and no injuries.
And I have a friend, a BHSI, who's run a riding school for 30 odd years, who pretty much does the same thing and has an exemplary safety record.
So like a lot of things with horses, it depends. Does the situation the OP described sound scary and unsafe? Yup. Is it always bad to start beginners jumping early? Nope. Depends on the conditions.