Why did the fellowship go south?

[Arvedui]

This question came to me when reading the 'Saruman's Caradhras motive' Thread. Why did they go south for Rivendell at all? They had to get to the eastern side of the Misty Mountains. By going south, their only options to be able to do so were, Rohan Gap, Moria and Caradhras.
The Rohan gap was close to Orthanc.
There was a Balrog in Moria, and they did not know if that road was safe.
Caradhras was not to pleasant a mountain.

They could have gone through the same High Pass east of Rivendell as they used in The Hobbit, and when they had crossed the Misty Mountains, go straight south towards Lothlorien.

Can't remember if this is mentioned in the book. If it is, I will probably hear it rather quickly.

[Eriol]

Well, I can't give you a quote, but I remember that someone (probably Gandalf) said that the orcs were multiplying again in the North after the Battle of the Five Armies, and the High Pass was closed for them. They hoped that the Dimrill Stair would still be free. This would be in the chapter after the CoE, 'The Ring Goes South'. This is just my memory.

Also, the lands on the other side of the Mountains were less wild, and they were afraid that they would be more easily spotted and hunted there. Again just my memory. It would be mentioned in the same chapter.

On the other hand, they did not know of the Balrog, and Caradhras' hostility was a surprise at that time of the year.

[Arvedui]

Thanks.
I just could not find that in the book. Grumble, grumble!

[Gothmog]

And one more point. The High pass was further north and would therefore have problems with snow earlier than would the Redhorn pass of Caradhras. So even without the problems of the Orcs, the time of year was against the High pass.

[Gil-Galad]

And because if you are in Rivendell Mordor is to the southeast of you,so it's obvious you should go to the south if you want to reach it!!