First of all, they are just establishing themselves in whatever role they are looking to follow in the future. If you take away study as a means of that establishment, they will not be able to prove themselves for that role. Some may find they don't have the opportunities, jobs, further study etc that they thought they would have.
But those opportunities will still be there once the crisis is over and the economy recovers. The next year - possibly the next couple of years - is going to be very tough for most of us. But if you want to present this as a
young vs old argument, then you could equally argue that younger people are likely to be at a point where their careers are more flexible and they have more working years ahead of them. Hence they may well, on average, be in a
better position than many older people to take advantage of whatever new opportunities present themselves in a few years' time.
Second, they have a greater proportion of their lives ahead of them than older people and are in the accumulation phase of life (knowledge, life changes, money) - simply stopping their lives for a year or so prevents that accumulation.
Surely it delays, rather than stops, that accumulation. Those opportunities to study and accumulate knowledge/experience/money/etc. aren't going away for ever. They are postponed, not destroyed.
Finally, because of that, they are the ones who are going to have to spend their whole lives paying for the costs which we have racked up in the last month.
I think your logic is incorrect. Say it takes X years for the country to pay off all the costs we have racked up. Then you can argue that anyone who dies within those X years is going to 'spend their whole life paying for the costs....' If - most plausibly - X is a decade or two, then that group will consist almost entirely of
older people, not younger people.
To be clear, I don't doubt that
many young people are badly affected by the current situation, just as many old people are badly affected. Everyone's circumstances are different, and there will be some people whose circumstances mean that the lockdown causes them more harm than others. But I don't think a simplistic trying to put groups of people against each other - such as young vs. old - is helpful.