At the Latin mass I go to the blood is not offered except to a family who cannot receive the host due to an extreme gluten intolerance.
If you are wondering why some parishes don’t offer the blood, it is because there isn’t a good way to offer the blood without everyone having to touch the chalice. Since the chalice is a sacred vessel it should only be touched by the priest. The priest’s hands were blessed at his ordination which is why he can touch the vessels.
In medieval times they would use very ornate, metal straws. The priest would dip the straw in the blood, put his finger on the top to keep the blood in the straw, and then release it into your mouth. This way no one but the priest had to tough the sacred vessel.
Pretty cool stuff!