I can't sign in onto my xbox 360 but I'm able to sign in on the xbox one

What an unfortunate issue. Although I do not know the solution first hand, I suggest contacting support via this link: https://beta.support.xbox.com/contact-us They
should have the answer you're looking for!

Hello, if you have the game console shared with a friend and your friend is the one with the Gold subscription, you will not be able to connect to Xbox 360 unless you have a Gold subscription, regards.

I already tried but I'm not able to sign in on the website. I see the "Sign in" thing but I can't click on it. And yeah, I already got Xbox 360 games in the past on my Xbox One.

You will be able to sign into xbox 1 and 360 using the same profile at the same time.

If I sign in to Xbox Live on my Xbox One, will I also be able to sign in on the same account on my 360 at the same time? Say someone is using the Xbox One in the living room and I'm playing my 360 in my bedroom. Will I be able to use the same account?

WHITTEN: Yes this works! You’ll be able to be signed on with the same gamertag on both an Xbox 360 and an Xbox One console at the same time. However, like today, you can only be signed into one Xbox 360 and one Xbox One at a time.

www.ign.com/.../ask-microsoft-anything-about-xbox-one

You can.

From IGN:

If I sign in to Xbox Live on my Xbox One, will I also be able to sign in on the same account on my 360 at the same time? Say someone is using the Xbox One in the living room and I'm playing my 360 in my bedroom. Will I be able to use the same account?
WHITTEN: Yes this works! You’ll be able to be signed on with the same gamertag on both an Xbox 360 and an Xbox One console at the same time. However, like today, you can only be signed into one Xbox 360 and one Xbox One at a time.

Link