Categorical Syllogism - Argument From Deduction

Who likes categorical syllogism?

I sure do.

Now, dont be scared by the name "categorical syllogism". 

Its actually not scary, but very simple form of logic.

All cats are animals.

All animals eat food.

Therefore, all cats eat food.

Simple, isnt it?

Its like math:

X = Y

Y = Z

Therefore

X = Z

Or in a different form:

X = Y

Z = X 

Z = Y

All people deserve human rights.

All gays are people.

All gays deserve human rights.

All gays are people.

All people deserve human rights.

All gays deserve human rights.

And that is categorical syllogism form of argument.

In the form of including, it goes:

Living beings include animals.

Animals include cats.

Therefore, living beings include cats.

Or in another form

Animals include cats.

Living beings include animals.

Living beings include cats.

The main problem that arises with syllogisms is when one of the premises proves too much. Take the example, "All people deserve human rights." The opposing side could argue that murderers or thieves forfeit their right to liberty and that the major premise is not valid. Your argument rests on both premises being valid, so you end up having to defend something completely off topic.

Gay is possible.

All people are possible

All people are possibly gay.

The closet door is is opening.

I understand that problems could arise if premise is false or easily disproven, or if you are forced to go off topic to defend it. But thats what usually happens in debates anyway.

However, categorical syllogisms are important, so I wanted to start with them.

You are going with

X includes Z

X includes Y

I includes Y

The conclusion doesnt logically follow.

It has to be in one of these forms:

X includes Y

Y includes Z

Therefore,

X includes Z

Or 

Y includes Z

X includes Y

X includes Z

It is better if:

Every individual is possibly gay.

All people are individuals.

All people are possibly gay.

Or

All people are possibly gay.

All individuals are people.

All individuals are possibly gay.

Why the "categorical" modifier, aren't your  examples just "syllogisms"?

Well there are three types of syllogisms.