Looking up how to root cuttings from things like figs, bay laurel, Japanese maples, and a variety of other plants, I’ve noticed that for some species you want to take cuttings from dormant, hardwood branches … for others, you want softwood, or semi-hardwood. Early spring. Late fall/winter. High summer. It’s hard to keep track & memorize!
What’s the botanical explanation behind why some plants root better when cuttings are taken under certain conditions?
The complex botanical answer: Plants is different. 
Apparently quite a few things will root this way. The past couple of years I’ve acquired a number of new figs as dormant wood cuttings - you can stick them in water until they begin actively rooting or (more commonly) I place them in moist potting soil and give them gentle bottom heat via a heat mat, loosely covering the pot in a plastic bag or enclosing potted cuttings under a vented plastic dome. Curiously, some fig varieties are easier to root this way than others.
This winter I’ve also gotten Vitex and hardy hibiscus to root from dormant wood cuttings.
Michael Dirr’s encyclopedic book on hardy shrubs and trees has useful information on propagation.
Some of it is plant hormones; what a cutting needs to do first is grow roots, but if the mother plant’s at a point where it’s flowering or preparing to flower, the hormone levels will be optimised for flower growth, which inhibits roots growth. Also, the hormone that triggers root growth is largely produced in the buds and young leaves, so if it’s all older leaves, there might not be enough for the cutting to grow roots fast enough to survive.
Or if it’s kinda not growing at all right now, but it’s still losing water through leaves, it’s not going to last long enough to grow roots. If it’s not got leaves and is dormant, it might stay hydrated long enough to kick into proper growth, but it depends a bit on what hormones will be produced in what quantity and order when it does break dormancy.
You can add artificial hormones, normally a powder or gel you dip the cutting into, to try to counter the natural production, or just give it a better chance, but plant hormone balance is really complicated and we still don’t understand all of what’s going on in even the most heavily studied plants.
It can be worth ignoring the rules and giving it a shot anyway, some of it honestly is based on ‘This is what the old head gardener always told me to do’. If the traditional way works, people sometimes just do that, don’t bother trying other techniques, and ignore people doing it differently.