It’s a simple question, but it’s not clear how to explain it

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Everyone is probably familiar with Bernoulli’s equation; in simple terms, the faster the flow rate, the lower the pressure. Essentially, it’s the law of conservation of energy, but there’s a contradiction I haven’t been able to figure out. Suppose there is a main pipe that supplies water outward, and there is a control valve on the end of this main pipe. When we open the control valve wider, the flow rate increases compared to before. This results in a decrease in the pressure of the main pipe; in other words, it is the situation where the flow rate is high and the pressure is low. But as everyone knows, when the control valve remains unchanged and the flow rate is to be increased, the only way is to raise the pressure, that is, to increase the pressure in the main pipe. Once the pressure in the main pipe increases, the flow rate rises as well, and the flow velocity becomes faster. These two theories are not contradictory; the first one deals with the relationship between flow rate and pressure, while the second deals with the relationship between flow rate and pressure difference (drop). Theoretically, they are not incompatible. However, from my analysis, in the second scenario, as the flow rate increases, the pressure in the main pipe should decrease – so why does it increase? Here, we need to analyze how the point for determining the pressure difference is chosen. Simply put, the pressure in my main pipe has increased. From this perspective, since the source of pressure has increased, the pressure difference should increase as well, which in turn results in a faster flow rate. If we consider only the pressure in the main pipe, an increase in pressure would lead to a decrease in flow rate. It’s quite contradictory, isn’t it? I’m not sure whether there’s an issue with the selection of the analysis points or with my understanding of certain definitions. It’s a simple question, but I just can’t figure it out. I hope my friends from Haichuan can explain to me where I went wrong.