Even on a jungle map, Ironworking isn't that big of a priority for me. Bronze working is an early tech and either my first or second goal. After that, though, I need to get some other techs, like the wheel if my resources aren't conveniently on rivers, one of agriculture/fishing/animal husbandry for my food resources, mysticism for city borders, masonry if I want to try for an early wonder, etc. If a city needs jungles cleared to be productive, I don't want to pay for it this early anyway.
If I find bronze that I can get a settler to, then there's just no way that I'm going to gamble on ironworking next; I might not even find iron where I can get to it. My cities can get their obilisk, barracks, and start pumping out units for the rush very early, with chop-rushing as needed and possible. The key to early war is to "get there fustest with the mostest", not to try to get a carefully balanced army of specialists. It's not a choice between whether to build axes and swords or just axes, but a decision about whether or not to even get swords.
Obviously, if you don't have bronze you can't axe rush, so you'd have to switch over to another plan. And other circumstances or UUs might affect this too; as the Romans you'd just go for iron, as Mansa you might just get archery and go with skirmishers, the Kahns would go for horseback riding (keshiks move 2 in all terrain, very nice for jungle), and so on.
Plus to whoever said you'd die if the enemy has horses and you build all axemen - building swordsmen don't help with that either, you need spearmen. Spearmen only require bronze, like axes, and come from a tech that's not on the way to ironworking. Plus you're probably having trouble with horses because you're giving your opponent time to research, connect, and build horse units by researching to iron, connecting it, and building swordsmen. I can have my axemen chopping at someome's capital before they can have enough horsemen to slow me down (though I usually mix in a few spears anyway if I have hunting).
A typical early tech path for me would be something like Mining, Bronze Working, mysticism, the wheel unless rivers cover it, Agriculture/animal husbandry/fishing, pottery, hunting-archery if no bronze, writing, alphabet, trade for stuff including ironworking.