An aggressive Paladin with good draws is really tough to beat. I'd think you'd stand a chance with all the Swipes and Sen'jin's you'd think you'd have something in time to not die. And if a Rogue can Sprint without dying in the next 2 turns, it's tough to beat so much card advantage. The downside to Sprint is that you have literally no board impact on turn 7, so you actually have to be in a pretty good board position to get it off.
There may have been some misplays on your part which are often hard to catch, since if you don't recognize them in time to play them, you usually don't see them later, and the impact is not immediately noticeable, so I can't comment on that, and I don't know what the other options were, but here are some comments on your draft:
- Wild Growth has a place in ramp Druids, which apparently are popular again, but it's pretty bad in arena. It's hard to get your curve off just right that you're really getting enough value for spending a card and your chance to impact the board on turn 2.
- 2x Mark of Nature almost has to be wrong. One, maybe. But 2? Paying 3 mana to add 4 stats to a minion is for the most part pretty unreasonable. 4 stats costs 2 mana and 0 cards (e.g. Yeti vs Raptor)
- Mogushan Warden is bad. Maybe playable if you're aggro and use it to get an extra hit out of a couple small minions, but it's going to be card disadvantage.
- Priestess of Elune is one of the worst cards in the game. I have to assume the other choices were Wisp and Grimscale Oracle or something.
Despite having 2 Ancients of War, you really lack good high-end stuff. You have no card draw and only 2 reasonably good big minions, so you have to be a little aggressive. Either you needed to draft that War Golem or other semi-weak big guy you passed on, or you need to have some moment where you turn on the kill switch and start hitting face. I would imagine this deck wants to get a good advantage around turn 4 with the strong turn 4 plays, put up a taunt, and start sending Swipes, Cat Druids, and Marks of Nature to the face before you run out of cards. I suspect running out of steam is what happened in your Rogue loss.