NAT provides some measure of security as pure coincidence to how it works. It is not designed or intended to provide security. It does not inspect packet payloads in order to filter them for security. It looks at the header and attempts to route it to an internal IP address (your devices on your LAN) and if it cannot, it will drop the packet because the header will only have the external IP address – the packet has no idea which device it is supposed to go to. Forwarding a port is telling the NAT to assume that when a packet hits a certain port, if it doesn’t know the destination internal IP, forward it to some internal IP anyway.

The reason you can connect to websites, ssh outside, FTP, whatever, is because your connection comes from your internal IP first to some other IP and therefore, NAT knows which internal IP to route those packets to.

Take for example this scenario:

You download some software. It has malware that provides command and control (C2) to someone else outside of your network. A firewall and/or antivirus may be able to stop this and hopefully notify you. NAT will not help here. Furthermore, if you have uPNP enabled (usually it is by default on your router) the malware can forward any ports through your NAT to the compromised device opening it up to bot attacks and the like.

Another scenario:

You want to play a video game with you and your friends and you’re going to host it. So either you manually forward those ports or perhaps uPNP just does it for you. That game has an exploit known by attackers, or perhaps it can just be DDoS’d. Your NAT isn’t going to stop that. Hopefully a firewall will help you here. It definitely will if you set up explicit rules so that if they aren’t your friend’s IPs it will drop them. Though it is possible the game is exploitable and your friend’s are compromised.

Take for example malware has been known to spread via Minecraft.