Everything is open source, which means security. If someone introduces a backdoor or virus, it can be spotted, which in itself is a reason not to do so. It isn't a black box, of which you cannot know what is going on inside.
This argument is arguable. For a small program, open source means security. For a larger system like Linux, open source is meaningless to security. Because no one (except the developer if the code is actively developing) will look into the code and spot the trojan / backdoor / virus. I recall that cryptsy claims (assume they are telling the truth) they are hacked by a coin, Lucky7Coin, and it is open source. I read some post describing on the code of Lucky7Coin. The hacker hides the backdoor in the C macro. No one awares of this backdoor until the hacker took away the money.
In the impression of general public, open source is safer. This is more like a marketing point in my opinion. Because 99.9999% users are not developers,. Even they can write code, they will not look into the open source.
I agree. I just didn't want to go too much in depth on each point. But I do think that having the source code open is like "come have a look, I have nothing to hide" and as such, is an indication of honesty. If the people who commit code are know real-world people, the likelihood is even higher that they are honest. It is certainly no guarantee, but on the other hand it is more of a guarantee than having a black-box with "there's no backdoors here, trust me".