Because just one language isn't enough.

Old Thuthic is a Satem language of the IE stock that is attested from the 900s AD in what is now Karelia. Its verbal system is Greco-Aryan in origin, but under influence from the surrounding languages has become much more transparent.

Since I'm starting to get tired, I'm just going to post some sound correspondences. Note that aspirates lengthen a preceding vowel.

*p -> f
*b -> p
*bʰ -> :p
*t -> θ
*d -> t
*dʰ -> :t
*ḱ -> š
*ǵ -> y
*ǵʰ -> :y
*k(ʷ) -> h
*g(ʷ) -> k
*g(ʷ)ʰ -> :k
*m -> m (but -> n word finally)
*n -> n
*s -> s
*w -> w (but -> Ø / C_)
*l -> r
*r -> r
*y -> Ø (but maintained word-medially)

The vowels develop as follows:

*o ō -> a ā
*Ṛ -> eR

Then:

*ĕ -> ɨ <ä>
*ĭ ŭ -> e o
*ā -> o
*ē -> e

Some numbers: enas, to, θres, häθor, fehä, säš, säftän, ašto, näwän, täšän, wešäθ, šäθan.

And some animals: äšwas, awäs, yos, mus, aršas, wärfo, wärhas, kos, sus, šo (genitive šonäs). A cookie to anyone who can decipher all of these before I wake up tomorrow.

quoting dhok, Priest, Norman, United States:

And some animals: äšwas, awäs, yos, mus, aršas, wärfo, wärhas, kos, sus, šo (genitive šonäs). A cookie to anyone who can decipher all of these before I wake up tomorrow.

Horse, sheep, [unsure], mouse, bear, fox, wolf, cow, pig, dog.
I really don't know what yos could be.

Looks like it'll be a pretty nice language.

The genitive of yos is yanäs, if that helps.

I'm going to skip doing anything about nouns right now, because I suspect Thuthic, like Tocharian, is going to drop a bunch of peripheral cases and then reinvent a whole bunch of new ones. Instead we'll look at the verbs.

Verbs distinguish past from present from future, perfective from imperfective (only in past tense), and indicative from "subjunctive" (really optative) mood. Originally this was along a Greco-Aryan line, but the system has become much more transparent under the influence of the surrounding Uralic languages.

The basic template is:

(augment)-stem-(perfective /s/)-thematic vowel-personal endings.

An active and a mediopassive exist. Endings:

Primary Active
-m    -mas
-š    -θä
-s    -:s

Secondary Active
-n    -mas
-s    -θä
-Ø    -n

Primary Mediopassive
-me    -meta
-se    -tä
-θe    -:θe

Secondary Mediopassive
-ma    -meta
-sa    -tä
-θa    -:θa

(A colon before an ending indicates that there was often a lengthening in the thematic vowel.)

(just realized I have a lot more shit to get done today than I thought I did, so I've got to go.)

quoting dhok, Priest, Norman, United States:

The genitive of yos is yanäs, if that helps.

Goose? I thought it might be, but without knowing more precise diachronics, it's hard.

No vowel harmony? I mean, come on, it's surrounded by Finno-Ugrics... ;-)

quoting hwhatting, Disinterest:

No vowel harmony? I mean, come on, it's surrounded by Finno-Ugrics... ;-)

So was Slavic- and /i e a o u ɨ/ is a pretty Slavic vowel system.

quoting dhok, Priest, Norman, United States:

quoting hwhatting, Disinterest:

No vowel harmony? I mean, come on, it's surrounded by Finno-Ugrics... ;-)

So was Slavic-

No, in its formative period, it wasn't. It had Iranian languages to the South, some Germanic adstrate, and to the North, Baltic languages; Baltic toponymy is attested as far East as Moscow and these (lost) Baltic languages formed a cordon that separated Slavic from Finno-Ugric until the northward expansion of Eastern Slavic (IIRC, during the 6th/7th century AD).
That said, I was joking; there's no law saying that a language surrounded by languages with vowel harmony has to acquire that feature. Just would have been an interesting and plausible development under the circumstances. :-)