Are external links unhealthy??

[motionz]

If I put I had to put an external link to my site's each and every page and post then, is it going to hurt my rankings??

In my opinion I will say that it totally depends in your site's type that it will hurt or not. If you have a general website which does not need any external links in each and every page then you will get penalized for sure.
But if your site needs external links for your site's actual purpose to serve then its safe. The point is that everything has to be very relevant. And, you should use the no-follow attribute also (in cases relevant) as well so it might not look like spammy.