Better way to swap elements in a list?

No need for complicated logic, simply rearrange the list with slicing and step:

In [1]: l = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

In [2]: l[::2], l[1::2] = l[1::2], l[::2]

In [3]: l
Out[3]: [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]

 TLDR;

Edited with explanation

I believe most viewers are already familiar with list slicing and multiple assignment. In case you don't I will try my best to explain what's going on (hope I do not make it worse).

To understand list slicing, here already has an excellent answer and explanation of list slice notation. Simply put:

a[start:end] # items start through end-1
a[start:]    # items start through the rest of the array
a[:end]      # items from the beginning through end-1
a[:]         # a copy of the whole array

There is also the step value, which can be used with any of the above:

a[start:end:step] # start through not past end, by step

Let's look at OP's requirements:

 [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]  # list l
  ^  ^  ^  ^  ^  ^  ^  ^  ^  ^
  0  1  2  3  4  5  6  7  8  9    # respective index of the elements
l[0]  l[2]  l[4]  l[6]  l[8]      # first tier : start=0, step=2
   l[1]  l[3]  l[5]  l[7]  l[9]   # second tier: start=1, step=2
-----------------------------------------------------------------------
l[1]  l[3]  l[5]  l[7]  l[9]
   l[0]  l[2]  l[4]  l[6]  l[8]   # desired output

First tier will be: l[::2] = [1, 3, 5, 7, 9] Second tier will be: l[1::2] = [2, 4, 6, 8, 10]

As we want to re-assign first = second & second = first, we can use multiple assignment, and update the original list in place:

first , second  = second , first

that is:

l[::2], l[1::2] = l[1::2], l[::2]

As a side note, to get a new list but not altering original l, we can assign a new list from l, and perform above, that is:

n = l[:]  # assign n as a copy of l (without [:], n still points to l)
n[::2], n[1::2] = n[1::2], n[::2]

Hopefully I do not confuse any of you with this added explanation. If it does, please help update mine and make it better :-)

Here a single list comprehension that does the trick:

In [1]: l = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

In [2]: [l[i^1] for i in range(len(l))]
Out[2]: [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]

The key to understanding it is the following demonstration of how it permutes the list indices:

In [3]: [i^1 for i in range(10)]
Out[3]: [1, 0, 3, 2, 5, 4, 7, 6, 9, 8]

The ^ is the exclusive or operator. All that i^1 does is flip the least-significant bit of i, effectively swapping 0 with 1, 2 with 3 and so on.