This is rule, you can see it from the link which bod gave.

the third person may not have any suffixes.

First personal pronoun: I - ben:
Ben gidiyorum << the suffix: -um
Second personal pronoun: you - sen:
Sen gidiyorsun << the suffix -sun
Third personal pronoun: he/she/it - o
O gidiyor- << no suffix.

Another example:

Ben öğretmenim
Sen öğretmensin
O öğretmen-

Or

Uçabilirim
Uçabilirsin
Uçabilir << no suffix.

If you are writing for your newspaper, if you are a journalist, you may add in your text the -dır suffix for the verb to be, or if you read something from an excyclopedia, you can see -dır suffixes for the third person. Or if you like literature and poem, you may find some examples with -dır suffix. But excepts these conditionals, -dır is not used much.

True in a case, false another.
Bu bir kedi also means "this is a cat."
Bu bir kadın also means "this is a woman"

I still do not understand the above statement

Singular Forms - Present
I am -im, -ım, -üm, -um
I am (After Vowels) -yim, -yım, -yüm, -yum
you are -sin, -sın, -sün, -sun
he/she/it is -dir, -dır, -dür, -dur
he/she/it is (Consonant Mutation) -tir, -tır, -tür, -tur

Omission of –dir and –dirler in spoken Turkish.

In spoken Turkish the third person suffixes, -dir and –dirler are usually omitted.

Examples:

Bu kitap çok kalın. - This book is very thick.

Bu tükenmez kalemler kırımızı. - These pens are red.

O çok uzun. - He is very tall.

Mehmet çok neşeli bir çocuk. - Mehmet is a very cheerful kid.

Onlar İngiliz. - They are British.



However, when giving information in a rather formal way, as opposed to making a mere personal observation, -dir and -dirler are used.

Examples:

İstanbul tarihi bir şehirdir. - İstanbul is a historical city.

Sezen Aksu ünlü bir şarkıcıdır. - Sezen Aksu is a famous singer.

Türkiye’nin başkenti Ankara’dır. - The capital city of Turkey is Ankara.


http://www.turkishclass.com/turkish_lesson_8

I am not being argumentative here, I am just trying to find out.

I said I think it makes a word formal or informal
if written it is usually included but omitted when spoke

http://www.turkishclass.com/turkish_lesson_8

seems to say this

I am not being argumentative here, but trying to find out the correct rule.

Rules are meant to be understood, that is why you have teachers, reading Turkish self study by Fono says the same as lesson 8 that they are there but seldom used in spoken words.

hasta-dır (s)he is ill
zengin-dir (s)he is rich
suçlu-dur (s)he is guilty
kötü-dür (s)he/it is bad
yasak-tır it is forbidden
garip-tir (s)he/it is strange
yok-tur there is no(t)
Türk-tür (s)he is a Turk

ie they are usually omitted, that does not make a rule, it is what happens in practice.

from lesson 8
In spoken Turkish the third person suffixes, -dir and –dirler are usually omitted

However, when giving information in a rather formal way, as opposed to making a mere personal observation, -dir and -dirler are used.


In English we write with grammer, but because people are lazy when they talk they don't always use grammar because it is implied in the context; this isn't a grammatical rule, it is just what happens.

I think this is what gives the confusion when you read a book like Fono and everything has dir (depending on vowel harmony) as a suffix but then hear no one using it.