I would also like to point out that if you have played other CCG before, it may seem odd to award the player going first because in traditional CCG they usually have the advantage, unlike in Gwent.
In Gwent, it's not that simple. When going first, you change from a reactive style to a proactive style, which can be an advantage or a disadvantage based on your deck and the opponents. For example, heavy control decks are reactive and are usually at a disadvantage going first.
I've noticed that a lot of the time players will simply surrender round 2 (having won round 1) because the may be a card or two down. [...] Seems a bit crazy to me that you work so hard to win a round then simply pass on the 2nd round to try and win the 3rd.
Ninja'd this from another thread because it's related to this.
Just like for some decks going first is an advantage, some decks thrive in a long round, while others do not and want a short round, instead. For example, engine-heavy decks tend to pass the second round (if they only have a few cards in hand) and go for a long third round. Most new players cannot take advantage of this and they do not know when to pass and when to push. This is one of the more tactical and challenging decisions of Gwent, which is difficult to master.
Why players want to win round 1 is because they want to dictate the narrative and decide whether they want to push for a 2-0 or go for a long round three. Mystic Echo (Francesca) Dwarfs or Harmony are notorious for pushing a 2-0. They win round 1 and then smack a quadruple Dwarf or Dryad engine on the board, which leads to an overwhelming head start and actually gives them the advantage when having to go first, in the second round. One last example is that you might want to bleed an engine deck in the second round, even when you have to go down a card in the final round because your finisher is stronger (like with tall Monsters).