Pirelli couldn't make a good tire for the life of them.
They've already admitted\told teams that 2017 tires will slow down the car by 2 seconds a lap.
As the tire can't take it and the only way round it is to increase the air pressure.
So the "5 seconds faster" has gone out the window. Bring back Bridgestone.
Pirelli are perfectly capable of building tyres to withstand the loads. What they said is they won't build tyres which won't incurring a penalty which will cancel out some of the gains the 2017 rules would introduce. If there was a tyre war they would be less inclined to build tyres which required much higher pressure - they'd go at it as they have done in the past.
The problem is we're in a control tyre situation and Pirelli won't tolerate another Silverstone 2013. If it was Pirelli vs Michelin on track I'm sure Pirelli would shed some of their concerns and start pushing the margins much as Michelin and Bridgestone did in their head-to-heads era.
The other problem, the bigger problem, is that the teams and FIA have been unable to come up with an agreement to allow Pirelli to test the tyres before the 2017 pre-season testing starts, so they'd be guessing on tyre design, so they'd have to play it safe for 2017 as things stand. It would be utterly ludicrous to do anything else.
It's not as simple as "here is the maximum load, build these". Every car (and even driver) uses the tyres differently and there are all sorts of factors to consider. Weight distribution, camber, lateral load, twisting load, torque, differential, rotational speed (as in top speed of the car) and so on. Without having a car to test with they can't begin to understand how any of these different forces will play out in 2017, so as things stand they'd have to build super-safe tyres. It wouldn't be any different if Michelin, Bridgestone, Dunlop or Avon were designing the tyres.
This is likely them putting pressure on the FIA and teams to come up with a solution to allow them to test a car which is likely to indicate what 2017 will bring.
And Bridgestone don't want to come back, so good luck persuading them otherwise.