Why shouldn't we simply keep our technology secret?

Sometimes that is the best option. Determining whether to go after a patent or to rely on trade secret protection is a very fact specific evaluation, but it can be the better way to go in some circumstances. One thing to be aware of is that if you do decide to keep the designs & code secret then you need to be prepared to really keep them secret. In order to maintain legal protection you need to make sure that you take reasonable steps to ensure the secrecy of the information. This can often be at odds with the need to advertise, get some publicity, and attract investors. Balancing the need to disclose with the need to keep things sufficiently secret can be tricky, but it can be a good option.

In addition to the answer provided by Mike, if somehow your designs and code became known, someone else could apply for a patent - the US went to a first-to-file system in March, 2013, so unless you can also prove that your designs and code were in place/in public/commercial use prior to this other person filing for patent, whereby your use would effectively be prior art to his patent application, they may receive a patent and then sue you for infringement. In addition, even without someone else getting a patent, if, again, your designs and codes were known to others, they could simply start using them without fear of infringing your patent because you would not have a patent.

I would also add that the trade secret protection varies strongly from one country to the other. The criteria for granting it and the respective damages are very country dependent.

A patent, on the other hand, offers a more or less similar protection in most countries.

Finally, as simple as it sounds now, actually keeping information secret is not that easy. As long as you are a few engineers in a room, friend and all, it can work rather easily. Once you grow to 50 people and you start having some people leaving, making sure they will not reuse the knowledge they acquired in your company is not easy, most of the time.