with which assertion? that it isn't Christian? or that it's Jewish?
Because by definition, it's impossible for the Old Testament to be Christian. To be pedantic, Christian, by definition, is "Christ Follower". If Christ had not been born on this earth yet, it is impossible for anyone to have been following Christ. Ergo, the Old Testament can't necessarily be "Christian". That is not, however, to say that we as Christians do not believe in the Old Testament. We see it as a quasi-historical record, with much that can be learned from that history. However the Christian faith really can't be defined as such until after Christ begins his ministry.
As to the Old Testament being Jewish, I would say that it's a history of the Jewish faith, but it's by no means the definition of the Jewish faith.
The Jews were looking forward to their Messiah and the OT is filled references and prophecies of the coming savior.
Jesus being believed in as the Messiah makes the whole OT Christian, it’s his story.
Jesus said that “before Abraham was, I am” claiming to be one with Jehovah by using a direct OT quote from God and applying it to himself.
“For unto us a child is born, unto us a son is given, the government shall be upon his shoulder: and his name shall be called wonderful, counselor, the mighty God, the Prince of peace.”
Christianity was initially considered a Jewish sect.