I like this quotation:

Teaching mathematics through informalism is like driving in a fog. One sees dim figures in the distance, and every once in a while some of them suddenly appear clearly, but usually everything is veiled and mysterious. It’s dangerous to drive in the fog, especially in a strange territory, and one must drive slowly. Even so, one may not always be sure where one is. Teaching rigor and precision, provided it is done without the veil of complexity interfering, burns away the fog, leaving everything crisp and clear and making it possible to drive faster and to enter uncharted lands.

When it is very clear what steps are legal, you can go further. Just like in programming, strong type systems will let you attempt things that you don't dare without them because you will probably fail somewhere without noticing.