Enabling/disabling 2nd texture unit

OpenGL OpenGL: Basic Coding
1

I had a little problem: once I enable and bind 1st and 2nd texture units I couldn’t disable 2nd texture unit simply writing
glActiveTextureARB(GL_TEXTURE1_ARB)
glDisable(GL_TEXTURE_2D)

It worked however after adding between above 2 commands this
glEnable(GL_TEXTURE_2D)
glBindTexture(GL_TEXTURE_2D, 0)

But do I always have to “unbind” (same as binding with texture 0 as OpenGL docs says) 2nd texture unit, when I don’t want to use it?
Is disabling not enough, or am I doing something completely wrong?

Thanks for clarification.