Hi,
it's a good question! "Путь" is a very special word. There is a simple explanation for that:

historically, "путь" used to be a feminine noun in Russian (old use: путь - она; длинная путь "a long way"). Yes, now it sounds weird for a modern Russian speaker.

But then, due to some reason, this noun changed its gender to masculine (modern use: путь - он; длинный путь "a long way"). But its declension forms still remind those of the feminine nouns ending in a soft sign.

Just compare three examples:

masculine
Nom. Sg. руль (steering-wheel)
Gen. Sg. руля
Dat. Sg. рулю
Acc. Sg. руль
Instr. Sg. рулём
Prep. Sg. (о) руле

Nom. Sg. рули
Gen. Sg. рулей
Dat. Sg. рулям
Acc. Sg. рули
Instr. Sg. рулями
Prep. Sg. (о) рулях

feminine
Nom. Sg. тень (shadow, shade)
Gen. Sg. тени
Dat. Sg. тени
Acc. Sg. тень
Instr. Sg. тенью
Prep. Sg. (о) тени

Nom. Sg. тени
Gen. Sg. теней
Dat. Sg. теням
Acc. Sg. тени
Instr. Sg. тенями
Prep. Sg. (о) тенях

путь (now masculine)
Nom. Sg. путь (way)
Gen. Sg. пути
Dat. Sg. пути
Acc. Sg. путь
Instr. Sg. путём
Prep. Sg. (о) пути

Nom. Sg. пути
Gen. Sg. путей
Dat. Sg. путям
Acc. Sg. пути
Instr. Sg. путями
Prep. Sg. (о) путях

It is the only noun which behaves this way. If you compare, you will easily find:
- in plural there is no difference in declension between masculine and feminine, so "путь" fits the pattern perfectly, and it is easy;
- in singular, "путь" behaves as a masculine noun in Instrumental;
- in singular, "путь" behaves as a feminine noun (but it is still masculine!) in other oblique cases (oblique cases are all cases except nominative and accusative).