'out loud' is a set phrase, 在这里loud不是形容词. 'I don't want to say it out' sounds 奇怪 in English

As vertices said, "out loud" is a set English phrase that means using your voice to say something, as opposed to just saying it in your head.

chū(1) lái(2)

因为我的猫不让我对别人告诉它。

I thought 出来 meant that the verb (说) was a completed action. I still do not understand how 'out loud' is implied. I put: I don't want to speak out. Can any native Chinese speakers clarify this sentence for us.

出來 are linked here. "Come out." 说出来 means that the speach is actually coming out of your mouth.

Look on Google for examples of directional compliments in Chinese. You should also look other verb compliments while you're at it. Like 说话,洗干净,etc. Those are similar.

Also, pro tip: any translation of these like go out, come over, go in, come in, are basically the reverse of what we say in English. 出去,过来,进去,进来。