It just isn't.
I can just about understand people who 'support' teams in other countries. I can more readily understand people who support their local non-league team (or their dad's, or whatever). These teams will either never meet in competition or will meet exceptionally rarely - a freak FA Cup draw or an unusual set of results that see them meeting in Europe.
But you can't support two teams that meet twice a season or more because they're in the same league in the same country. As soon as you want your team not to win, you're not supporting them, and if your two teams meet you either want one of them to lose (so you don't support them) or for them to draw (so you don't support either of them).
Next weekend, Sheffield Wednesday play Fulham. Fulham may be the most dangerous team in the playoffs, with the highest amount of goals scored in the division* and if we lose or draw, we will avoid meeting them until the playoff final - thus standing the best chance of getting to the playoff final and then on to the Premier League. If we beat them, we will face them in the playoff semi-finals and stand a higher chance of being knocked out.
I want us to win, because I support the team and want us to win every game. And if we beat them once, we can beat them again (and then again).
*They're probably thinking exactly the same thing about us - we've won six in a row, kept 16 clean sheets and have the lowest goals conceded outside the top two, with the Championship's record goalscorer, two Scottish internationals and Fernando Forestieri up front.