Why did Zach get angry at Bryce in this particular scene?

Because he didn't follow the pitching instructions he was given

In case you don’t know how baseball works, the catcher calls the pitch and the pitcher either waves it off or agrees and throws the pitch the pitcher throws. Zach called a change-up, yet Bryce continued to defy him by throwing fastballs. He also didn’t wave off the pitch. Because Bryce does whatever he wants, when he wants it, Zach walked off the field in the middle of the game towards the clubhouse.

Source

The simplistic answer would be that baseball players are supposed to be a team and act like a team. It is easier to perform like a team when teammates know what to expect from one another. There is little room for star player to showboat due to ego or pride.

It is also easier to catch a small object moving at a high rate of speed when you can anticipate where it is supposed to be. A catcher missing a ball can cause a play at home plate that would allow the other team to score.

The more complex answer is that there is a hierarchy on a baseball team. A great example of this hierarchy can be seen in the movie Bull Durham. The pitcher is the technician (Head or Star Employee). The catcher is the tactician (Frontline Manager / Team Lead). The coach is the strategist (COO). The general manager is the logistician (CFO). The owner is the commander-in-chief and primary stakeholder (CEO). The other field players are support and defense. The batter is an attacking aggressor from the enemy offense. The batter lineup is the frontline of the enemy under the command of the enemy coach/strategist.

• Primary stakeholder/Commander-in-chief (CEO) - The owner provides the resources to develop the team and the guidance to grow it into a valuable and profitable organization. The owner reaps the rewards of this growth and development. The owner also supervises the general manager to achieve this end.
• Logistician (CFO) - The general manager manages the resources provided them and plans for both the near and far future. Their job is to put the team into the right position and best opportunity to be a winning franchise by winning seasons. Doing this consistently will grow the value of the team. The general manager supplies the coach with these resources (including personnel). They then supervise the coach to achieve the end goal.
• Statistician (COO) - The coach uses the resources given them to acquire, develop and lead personnel. Their job is to use their leadership to win the season. Their goal is to have a winning franchise. Their focus is on the current and next seasons. They win the season by winning individual games. The coach supervises the catcher (and other coaches and players) to achieve this goal.
• Tactician (Frontline Manager / Team Lead) - The catcher’s job is to win games. They do this by studying and planning for each batter. The catcher has to know each batter and their own pitcher (their strength, weaknesses, patterns, and trends). The catcher also have the best view of the whole field of play from a defensive point of view. From there, the catcher can use that knowledge and cues from the coach to relay signals to the pitcher on what pitches to throw (the hand signals you mentioned in your question). Their position is often called the thinking-man’s position. The catcher has to make decisions without pride, ego, or the heat of the moment getting in the way. The catcher, in essence, supervises the pitcher. That is why when a pitcher gets removed/relieved from the game by their own team, the catcher comes out to the pitching mound as well as the coach.
• Technician (Head or Star Employee) - The pitcher’s job is to deliver the baseball where and how he is told. His job is to focus on each and every individual pitch. His concentration should not be broken by what’s going on around him on the field or off (even in his personal life). He must focus on the pitch he is currently throwing and forget about any previous or future pitches (even to the same batter. It is all about precision at that moment. A good example of this can be seen in the movie For the Love of the Game.

Your character, Bryce, was stepping out of and breaking the hierarchy. This could have potentially cost them the game. Luckily, it didn’t.