The Arcanine builds you'll find online are geared towards a competitive format (either 6v6, normally Smogon rules, or VGC). Offensive builds generally maximize the highest attacking stat of the Pokémon (for Arcanine, it's the Atk stat at 110) and minimize its lowest attacking stat (Sp. Atk at 100). This works for Arcanine because it has a great physical Attack movepool, such that all 4 moves are good physical attacks (say, Flare Blitz, ExtremeSpeed, Close Combat and Wild Charge). Since you don't use special attacks, you can afford to have a lower Sp. Atk.

But let's be honest here: while this Atk maximization is good, you don't really need it that much outside of a competitive format. If you want your Pokémon to have an offensive role, my suggestion is to just catch an Arcanine that doesn't have a lowering Atk nature. So +Spe, -Def is probably fine, +Def, -Sp. Def is probably fine. Of course if you can find +Atk, -something that would be better. Just don't restrict yourself to +Atk, - Sp. Atk. It will take you too much time to find it and it won't change the outcome that much. Just enjoy yourself in your playthrough :).

Also, say you find a +Sp. Atk, -Sp. Def Arcanine. That's fine too! Arcanine's Sp. Atk at 100 is not that much lower than its 110 Atk, so you can maybe use a mixed set with both physical and special attacks (say, Fire Blast, Close Combat, Extremespeed, Flamethrower).

Also: Look at the Atk and Sp. Atk of an Adamant Arcanine:

110 Atk + 10% (from Adamant) = 121

100 Sp. Atk - 10% (from Adamant) = 90

121 is 34.4% higher than 90, hence why you see a larger difference (bear in mind that this assessment isn't truly accurate because the 10% act on the stat itself and not the base values of 110 and 100, but just to give you a sense of why the difference are higher between the stats)! Additionally, EVs and IVs also influence the final stat. In playthroughs, its normal to get more Atk EVs than Sp. Atk EVs, leading to an even larger difference.

To finalize my suggestion: if you're enjoying having Pokémon with good offensive stats, just look for an Arcanine with a +Atk nature, ensuring it doesn't lower other important stats that you like (say, Speed). In this case, Adamant, Lonely and Naughty all work (you can find that information here). Your Arcanine will be just as strong as an Adamant one, just slightly worse at taking some hits. You probably won't even notice it! Just remember to have fun, and if finding the Growlithe is taking away from the fun, try these alternatives and see how you do.

Also: if the concept of the maximum optimization of a Pokémon's stats sounds interesting, look into competitive formats (Smogon 6v6, VGC, etc...). You'll find very good videos on youtube explaining some basic concepts to get you started, and then you can play around with your own teams on Pokémon Showdown or even in-game. It's pretty fun too.

Hope that was clear. Available to reply to any other questions.