You can only have one power output per net, so it is joining the two that is causing the problem.
Usually you only have a “power out” pin on something really simple like a linear regulator, on connectors and more complex power supplies (e.g. switch mode) they don’t work for design rule checking.
The way to get around this is to add “PWR_FLAG” from the “Place power port” tool once to each net that needs to be driven. When you place it, make sure there really is a driving source (in this case your ATX 12V connector) and then just connect the power flag to the +12V net.
The power flag component isn’t a component symbol or power port in the normal sense, it just provides a driving source for the purpose of verifying the design. Generally I put these off the page somewhere, they’ll still get taken into account when the electrical rule check is run but aren’t in the schematic output if you print/plot it.