Won't reopening the economy restart the Virus?

It could "restart" the virus, but right now, that's a moot point. Since the virus has not gone away, reopening the economy won't 'restart' the virus.  Nothing has changed; the virus will simply continue to spread.

You're not wrong. You're absolutely correct.

It could quite easily rejuvenate virus spreading, yes.  That is the major concern.  The idea that most governments appear to be following is that once the virus growth rate stops increasing (the acceleration of the growth stops, and spreading starts to slow) THEN we can start to slowly reopen the system, as long as it is done in ways that does not allow the virus to regain accelerated growth.

That is what the mean about flattening the curve and reaching peak.  At some point, the amount of new cases will start to be less than the days before.  This will, a few weeks later, lead to fewer deaths per day than the previous days.  We aren't there yet in most places, even if the growth rates have slowed considerably (the curve has been flattened).

Reopening social interactions too fully will just let the dang virus retake hold.

Not restarting the economy will cause people to get violent and kill each other. [ Think French Revolution. ] America must pick its poison. The CV will be here until a good vaccine is developed and administered,

Reopening too soon can cause a resurgence but no one knows what will happen until it is tried. And yes, reaching a peak is not the end. The peak is when the rate of increase in whatever is being measured begins a steady decline. The actual numbers of cases and deaths will always go higher with each new one until there are no more, and that will come some time after the peak is reached.

If reopening is not done with necessary precautions and safeguards, experts fear it could lead to a second wave that could be worse than the first. That's why testing is so important, as well as continuing things like social distancing that are know to diminish the spread of the disease.

Yes, you're right, but the point is to spread out the infections so that hospitals and healthcare workers aren't overwhelmed. Eventually, a high percentage of people are going to have to have the virus and recover from it to give us herd immunity. It's just a real problem if we all get it all at once. 

people will still have to wear masks for a while and keep their distance as much as possible. you can't throw the baby out with the bathwater, which means destroying the economy to keep people safe. they MIGHT be safe, but they won't be happy and free to live their lives. getting this virus is not a death sentence. I had it and if you catch it early and begin a vigilant cold or flu regimen, you'll survive it. But we need to get back to work! We can't keep paying people not to work, that's communism.

Reopneing the economy doesn't mean completely ending the lockdown.

You can "reopn" gradually, allowing some businesses to take measures which allow them to start delivering goods again.