I get that there is turbulent air flow behind a car but I don't get why following a few yards behind a car makes it very difficult to overtake and is damaging for the following cars' engine and tyres but yet a few yards further back again there can be a slipstream effect.
Turbulent air from the car in front affects the wings and stops them working as well as they should.
Because wings produce both downforce and drag, this has two effects : the reduction in downforce means lower cornering grip, while the reduction in drag means higher straightline speed.
If the straight is long enough, the driver can take advantage of the lower drag and overtake before the corner and before the lower downforce becomes a probem for him, but the problem is when circuits - particularly the newer ones - have a lot of corners linked by short straights and there simply isn't enough space to take advantage of the slipstream effect before the corner, and then the lower downforce hurts him too much that he can only get so close. Because of circuit design the downsides (lower grip) usually outweigh the upsides (higher straightline speed) by a massive margin, and overtaking is impossible.
Note that on circuits like Monza (long straights, few corners) then slipstreaming happens a lot more - there is room on the straights to do it, and because there are so few corners the penalties are reduced. This is why newer circuits - with the Tikle-clone long pit-straight but also with lots of tight corners linked by short straights - have problems. Because there are so many corners the effect of losing the downforce is multiplied, and the single long straight is not enough to make up for it.
It is this "only getting so close" that is the problem that F1 has tried to tackle in recent years with repeated rule changes (plus proposed new ones, see here
), but most people say circuit design is the bigger problem.
Some say it's the wing settings that are the problem, but it's the circuit that dictates the wing settings. If there's a lot of corners then teams will crank on the wing and the problem is made worse - note how F1 never saw as much overtaking as they hoped when they raced at Indy : the tight, twisty infield section made teams increase the downforce, so they couldnt slipstream as much as the Indycars could on the straight.
So to answer your question, when the car is far behind the guy in front, he gets the benefit but not the downside. When he gets closer, the gets the downside, and this more than cancels out any benefit.
Glacierre makes a great point about NASCAR - although they have small wings and front splitters, they are more about highspeed stability than downforce, plus they race mainly on ovals, so slipstreaming happens a lot more.