To center horizontally this should be enough

button.pack(side=TOP)

But to center horizontally and vertically you could use nested frames. Check the following script:

import tkinter as tk

#%% Frames
frameA = tk.Frame(background="#c8c8c8")
frameB = tk.Frame(width=200, height = 200, background="#646464")
# Nested Frame. framebb is created within frameB without width or height
framebb = tk.Frame(frameB, background="#646464")
frameC = tk.Frame(width=100, height = 100, background="bisque")

frameA.pack(side='top', fill=None)
frameB.pack(side='top')
# expand is the key parameter to center the framebb within frameB
framebb.pack(expand=True)
frameC.pack(side='bottom')

#frameA.pack_propagate(False)
frameB.pack_propagate(False)
frameC.pack_propagate(False)

#%% Buttons and Labels
tk.Label(frameA, text = "Text within the frame A").pack()

a = tk.Button(framebb, text = "A").pack()
b = tk.Button(framebb, text = "B").pack()
c = tk.Button(framebb, text = "C").pack()
d = tk.Button(frameC, text = "D").pack()
e = tk.Button(frameC, text = "E").pack()

tk.mainloop()

Another approach could be using the .grid() method

button.grid(row=1,col=0)

the values of row=1,col=0 depend of the position of the other widget in your window

or you can use .place(relx=0.5, rely=0.5, anchor=CENTER)

button.place(relx=0.5, rely=0.5, anchor=CENTER)

Notice that the parameter anchor is referencing the a relative position to the object (in this case button). anchor is not referencing to a position in the window. You could think that the button is a ship that has several anchors so you should choose a coordinate and which anchor you want to fix in that coordinate.

Example using .place():

from tkinter import *  # Use this if use python 3.xx
#from Tkinter import *   # Use this if use python 2.xx
a = Button(text="Center Button")
b = Button(text="Top Left Button")
c = Button(text="Bottom Right Button")

# You can use the strings the referencing the relative position on the button
# strings = n, ne, e, se, s, sw, w, nw, c or center
# Or you can use the constants of tkinter
# N, NE, E, SE, S, SW, W, NW, CENTER
a.place(relx=0.5, rely=0.5, anchor=CENTER)
b.place(relx=0.0, rely=0.0, anchor=NW)
c.place(relx=1.0, rely=1.0, anchor=SE)
mainloop()

Actually in the previous semester I have also made some Tkinter application which is the project given by teacher to us. So I go to some tutorials website of Python and find three methods of placing the widgets on the output screen. The three methods are

 1. Pack()
 2. Grid()
 3. Place() #the best method over Pack() and Grid()

Place() method take the coordinates in the form of the x and y. See this link for more clarification https://www.tutorialspoint.com/python/python_gui_programming.htm

https://www.tutorialspoint.com/python/tk_place.htm

See the bottom of the Page of the given link.The Place() method is defined with its proper arguments. I will prefer the Place() method over Pack() and Grid() because it works like CSS as we use in html, because it take the value of (width,height) and place your widget according to wherever you want.

If you find your answer a thumbs up will be appreciated.

Causing a widget to appear requires that you position it using with what Tkinter calls "geometry managers". The three managers are grid, pack and place. Each has strengths and weaknesses. These three managers are implemented as methods on all widgets.

grid, as its name implies, is perfect for laying widgets in a grid. You can specify rows and columns, row and column spans, padding, etc.

Example:

b = Button(...)
b.grid(row=2, column=3, columnspan=2)

pack uses a box metaphor, letting you "pack" widgets along one of the sides of a container. pack is extremely good at all-vertical or all-horizontal layouts. Toolbars, for example, where widgets are aligned in a horizontal line, are a good place to use pack.

Example:

b = Button(...)
b.pack(side="top", fill='both', expand=True, padx=4, pady=4)`

place is the least used geometry manager. With place you specify the exact x/y location and exact width/height for a widget. It has some nice features such as being able to use either absolute or relative coordinates (for example: you can place a widget at 10,10, or at 50% of the widgets width or height).

Unlike grid and pack, using place does not cause the parent widget to expand or collapse to fit all of the widgets that have been placed inside.

Example:

b = Button(...)
b.place(relx=.5, rely=.5, anchor="c")

With those three geometry managers you can do just about any type of layout you can imagine.

I made some changes to your code below that seems to center the buttons like you're looking for. I removed the fixed geometry, the window will size itself. You also were mixing pack and grid, which can cause headaches like this to occur. It is best to pick one method and stick with it. Giving the first column in the header Frame a weight of one will make the label expand to fill all available space, centering it in the column.

from tkinter import *

home = Tk()
home.title("Home Page")
# Removed fixed geometry
home.resizable(0,0)

header = LabelFrame(home, bg="#12a8e3")
content = LabelFrame(home, bg="white")

header.columnconfigure(0, weight=1) # Forces column to expand to fill all available space

title = Label(header, text="School Subjects Quiz", bg="#12a8e3", fg="white", font=("Ariel",35, "bold"), padx=10, pady=10)
title.grid(row=0, column=0, columnspan=3) # Changed from pack to grid for consistency

questionsButton = Button(content, text="Questions", padx=250, pady=150)
questionsButton.grid(row=1, column=0, columnspan=3, padx=50, pady=50)

accountButton = Button(content, text="Account", padx=150, pady=150)
accountButton.grid(row=2, column=0, padx=50, pady=50)

resourceButton = Button(content, text="Revision Resources", padx=150, pady=150)
resourceButton.grid(row=2, column=1, padx=50, pady=50)

header.grid(row=0, sticky='NSEW')
content.grid(row=1, sticky='NSEW')

home.mainloop()