However for most native birds in my country even a spot of an acre or two can be a good bird habitat for nesting and feeding and birds will happily overfly humanity to get to and fro.
The smaller species of plants and animals in the forest food chain migrate slowly - perhaps a few inches or feet a year, and forest edges are different. Not least they have vastly more light than within the depths of the forest. The carbon uptake is less - thanks to that increased light, the decomposition cycle is different, and less of the dead wood gets broken up to go deep into the soil. By creating lots of little islands with only edge forest, you no longer have the true forest - that far enough into the canopy that deep forest rules apply - the forest that in theory we wanted to save. A connecting strip between areas risks multiplying that edge forest effect dramatically - trapping deep forest species just as surely as an eight lane road or city in the way.
Without a contiguous forest in which to exist, those isolated islands start to evolve differently. In the case of tropical and temperate rainforest you need the huge expanse or you lose the climate impacting effects. e.g. one tree takes up some number of litres of water in the growing season, and you need n trees to seed enough clouds to remain rain forest, or put enough terpines in the air (particularly coniferous) to preserve the right balance of insects.
It's these climate impacting effects - the water uptake and cloud seeding, that is one of the main reasons many studies are claiming the Amazon is nearing a tipping point into catastrophic drying.
TL;DR we really need to develop the will to preserve and remake unfragmented, untouched - or at least limited - wilderness forest - for the benefit of all of us.