In Jesus' time, the tithe could not go to Christ ministry because the law would not allow it. The tithe was a Levitical non-transferable inheritance. If Christ had requested a tithe, he would have been stealing from the Levites who had the commandment from God to take an edible tithe from the people as the book of Hebrews establishes. Jesus was not a Levite and therefore was not authorized to take or accepts tithes. The Bible talks about giving but not about tithing money.
