Why overriding mousePressEvent in PyQt makes clicking signal doesn't trigger?

The event isn't being propagated because you have accepted it in your handler.

You allow need to call the the original handler.

FWIW, you can hook up a handler to itemSelectionChanged and get the selectedItems on the table rather than tracking positions.

import sys
from PyQt5.QtWidgets import (
    QApplication, QWidget, QTableWidget, 
    QTableWidgetItem, QGridLayout
)


class Widget(QWidget):

    def __init__(self):
        super().__init__()

        self.initUI()    

    def initUI(self):
        self.setGeometry(300, 300, 300, 220)
        self.setWindowTitle('Simple')

        table = TrackedTableWidget()

        layout = QGridLayout()
        layout.addWidget(table, 0, 0)
        self.setLayout(layout)

        self.show()


class TrackedTableWidget(QTableWidget):
    def __init__(self, *args, **kwargs):
        super().__init__()

        self.initUI()    

    def initUI(self):
        self.setRowCount(2)
        self.setColumnCount(2)
        self.setItem(0, 0, QTableWidgetItem('30', 0));
        self.setItem(0, 1, QTableWidgetItem('40', 0));
        self.setItem(1, 0, QTableWidgetItem('50', 0));
        self.setItem(1, 1, QTableWidgetItem('60', 0));

        self.cellClicked.connect(self._handle_cell_clicked)
        self.itemSelectionChanged.connect(self._handle_item_selection)

    def _handle_cell_clicked(self, row, column):
        print('cell_clicked', row, column)
        print('selected cell positions', self.startingposx, self.endingposx)

    def _handle_item_selection(self, *args):
        print(self.selectedItems())
        print('item_selection', args)

    def mousePressEvent(self, event):
        print('mousePressEvent')
        self.startingposx = event.x()
        super().mousePressEvent(event)

    def mouseReleaseEvent(self, event):
        print('mouseReleaseEvent')
        self.endingposx = event.x()
        super().mouseReleaseEvent(event)

if __name__ == '__main__':

    app = QApplication(sys.argv)
    widget = Widget()

    sys.exit(app.exec_())

Reference

• About accepting events