It is from two intuitive reasons ..
The big part is how tension works .. have you noticed when two droplets of water in say a glass surface meet? .. the bigger droplet always seems to ‘suck’ the smaller droplet when they merge .. thats because the bigger droplet has lower pressure inside it! .. same with balloons .. think of it this way, if you were to allow balloons/droplets to merge, if the bigger sucks in the smaller droplet, it will only slightly get bigger, so no much change in pressure/energy required, while the smaller one get to be completely flat so all the pressure there can be gone! .. this is because the energy required to hold pressure depends on surface area which grows slower than the volume inside .. hence spheres held by surface-tension (like a balloon or droplets) have lower pressure in them the bigger they get!
The second part is simply that rubber is a type of material that can be ‘preconditioned’ .. basically if you stretch a balloon several times before you try to blow into it, you’ll find its a lot easier to get it started! .. all the stretching you do before hand ‘loosens up’ the rubber (and makes it warmer etc) and if you dont do that it is stiffer and therefore harder to blow up!
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