How to run all PyTest assertions even if some of them fail?

It ran all of your tests. You only wrote one test, and that test ran!

If you want nonfatal assertions, where a test will keep going if an assertion fails (like Google Test's EXPECT macros), try pytest-expect, which provides that functionality. Here's the example their site gives:

def test_func(expect):
    expect('a' == 'b')
    expect(1 != 1)
    a = 1
    b = 2
    expect(a == b, 'a:%s b:%s' % (a,b))

You can see that expectation failures don't stop the test, and all failed expectations get reported:

$ python -m pytest test_expect.py
================ test session starts =================
platform darwin -- Python 2.7.9 -- py-1.4.26 -- pytest-2.7.0
rootdir: /Users/okken/example, inifile: 
plugins: expect
collected 1 items 

test_expect.py F

====================== FAILURES ======================
_____________________ test_func ______________________
>    expect('a' == 'b')
test_expect.py:2
--------
>    expect(1 != 1)
test_expect.py:3
--------
>    expect(a == b, 'a:%s b:%s' % (a,b))
a:1 b:2
test_expect.py:6
--------
Failed Expectations:3
============== 1 failed in 0.01 seconds ==============

As others already mentioned, you'd ideally write multiple tests and only have one assertion in each (that's not a hard limit, but a good guideline).

The @pytest.mark.parametrize decorator makes this easy:

import pytest

def parrot(i):
    return i

@pytest.mark.parametrize('inp, expected', [(0, 0), (1, 1), (2, 1), (2, 2)])
def test_parrot(inp, expected):
    assert parrot(inp) == expected

When running it with -v:

parrot.py::test_parrot[0-0] PASSED
parrot.py::test_parrot[1-1] PASSED
parrot.py::test_parrot[2-1] FAILED
parrot.py::test_parrot[2-2] PASSED

=================================== FAILURES ===================================
_______________________________ test_parrot[2-1] _______________________________

inp = 2, expected = 1

    @pytest.mark.parametrize('inp, expected', [(0, 0), (1, 1), (2, 1), (2, 2)])
    def test_parrot(inp, expected):
>       assert parrot(inp) == expected
E       assert 2 == 1
E        +  where 2 = parrot(2)

parrot.py:8: AssertionError
====================== 1 failed, 3 passed in 0.01 seconds ======================

The pytest plugin pytest-check is a rewrite of pytest-expect (which was recommended here previously but has gone stale). It will let you do a "soft" assert like so:

An example from the GitHub repo:

import pytest_check as check

def test_example():
    a = 1
    b = 2
    c = [2, 4, 6]
    check.greater(a, b)
    check.less_equal(b, a)
    check.is_in(a, c, "Is 1 in the list")
    check.is_not_in(b, c, "make sure 2 isn't in list")