Nerd here: I often wonder what people mean when they say "secure". I'm paranoid, so I'm a lot more worried about data being intercepted, stored, and mined than I am about someone picking up my phone and seeing my gf boobs.

What I tend to look for is end-to-end encryption. Feel free to read on it on Wikipedia if you don't know what it is. If I'm 'mansplaning' here, someone please slap me. Basically I look for end-to-end encryption bc it was designed to send your messages in a way that ONLY the destination can see it.

Couple, for instance, is a really good app for privacy, but it says in their terms of service:

We may, and you hereby authorize us to, disclose your Personal Information (including messages) to a third party without your consent:

Its important to know that they will not do anything with your messages unless you're suspected as a terrorist or something extreme, but if we're talking security, they, as a company, can still sniff your messages. If they can, maybe someone else can?

I don't wanna make anyone paranoid, I'm just a paranoid nerd here that is a huge supporter of e2e encryption. I do highly recommend Couple. Though if you wanna make sure that ONLY your recipient can see the message you send them, I would really recommend WhatsApp because they implemented e2e not too long ago. However, WhatsApp is not a password protected app so I guess I can't have the best of both worlds.

EDIT: I also wanted to mention that Couple and Between us does offer Secure Socket Layer in their messaging. The likelihood that a hacker can intercept your message and decrypt it is minimal. Also Between Us does encrypt your photos on their server