The reason is essentially mathematical. Imagine 1000 get covid and 5 days later test positive. At that point no one has died at all and in fact maybe nobody dies for two weeks.
After a few weeks some of them start dying and eventually 10, say, die and a number of others are still horribly ill.
That is bad but maybe acceptable.
Now imagine that every week the number infected doubles.
In week one no one dies. At the end of the week there are 2000 cases. At the end of week 2 still no one dies but there are now 4000. At the end of week three a few people die from the start of week one and there are 8000 cases. At the end of week four maybe 10 die who caught it in week one and there are 16000 cases. At the end of week five 20 people have died and there are 32000 cases. At the end of week 6 40 have died and there are 64000 cases. At the end of week 7 80 have died and there are 128000 cases.
Now at this point the number who have died is not that great. But even if no one else ever got infected we can expect 1280 to die in the next month or so. However much worse than that, if we don't lock down then in another 3 weeks 1 million will be infected and we are guaranteed approximately 10000 deaths in the subsequent months.
So when was the right time to lock down? Was it at week 7 when only 80 people had died but 1280 were going to die? Or should we have locked down much earlier?
In essence, in this scenario with doubling infection rates, whenever you lockdown is too late.
The right time for lockdown in the UK the first time was probably March 1. But who would have accepted it?