A concept in strength training, we generally understand understand "pushing to failure" to mean pushing out as many reps as possible while using good form, until you reach the point where you can't keep that form.
When you fail to keep good form, that's when you know you've pushed enough.
Painful and tiring, pushing to failure is only the first part of the equation, the other half being rest.
Muscle growth and strength gains happen after you push to failure and then rest and recover.
With awareness and intent, it's the same with anything we put ourselves into.

• Keep to good form (best practices, best effort, quality work) while working things out.
  
• Gain strength and grow in the aftermath of stressful events, leave yourself time to rest and recover (and learn) from these events.
  

The important thing to remember is to choose to learn everything we can from the hard work-outs, the hard lessons, when we rest.
Don't just walk away with the memory of pain.
We have a learned reaction to making mistakes.
It's "Oops, avoid," or "Watch out!" Mistakes are associated with embarrassment (and being one), failure (and being one), feeling stupid, losing face, etc.
So when even the thought of making a mistake can cause you to cringe, take a step back and ask yourself what's really going on.
Is it you talking, or is fear taking charge of your decisions? Fear of failure is something we learn - it's artificially induced.
Failing is not a sin (look at one definition - hamartein ).
We just missed the mark we were aiming for.
It's not us who are failures, it's just an action you took that didn't work out, a decision that didn't have the expected results.
What are the benefits of resting after having "missed your mark"?

• You gain strength in the resting stage not when you're actually stressing.
  The stressful event will require your attention and focus, but in its aftermath (the rest period) you can recover and study the after effects of your actions.
  Don't push it all behind you.
  Squeeze the lessons out if you have to, so you know what to to to better protect yourself in the future.
  
• You can increase tolerance for stress and build an increased capacity to deal with crises.
  You did it before, you can do better now that you learned from experience.
  
• You learn what you can do and what you're capable of, so you can work a little easier the next time a similar issue comes around.
  

So don't be afraid of mistakes, just be careful of not learning from them.
Learn, push again, and rest before starting over.