Special connection with animals
I had a similar experience when I wrote a program that would kind of simulate the experience of past lives that the Buddha talks about.

It randomly distributes your previous births
around various kinds of beings into the distant
past:

+--------------+------------+------------+------------+
|    Being     |    Born    |    Died    |    Age     |
+--------------+------------+------------+------------+
|    adult     | 1983-07-13 | 2014-08-16 | 31.1 years |
|     crab     | 1979-08-02 | 1983-07-13 | 3.9 years  |
|     crab     | 1975-06-23 | 1979-08-02 | 4.1 years  |
|    insect    | 1974-11-12 | 1975-06-23 |  7 months  |
|     worm     | 1970-05-15 | 1974-11-12 | 4.5 years  |
|    insect    | 1969-06-21 | 1970-05-15 | 11 months  |
|     worm     | 1963-11-23 | 1969-06-21 | 5.6 years  |
|     crab     | 1960-01-17 | 1963-11-23 | 3.9 years  |
|    insect    | 1959-10-06 | 1960-01-17 |  3 months  |
|    insect    | 1958-10-29 | 1959-10-06 | 11 months  |
|    insect    | 1957-09-30 | 1958-10-29 | 1.1 years  |
|    insect    | 1956-03-17 | 1957-09-30 | 1.5 years  |
|    insect    | 1956-02-02 | 1956-03-17 |  1 months  |
|     worm     | 1951-02-19 | 1956-02-02 | 5.0 years  |
|    insect    | 1950-09-03 | 1951-02-19 |  6 months  |
|    insect    | 1950-03-03 | 1950-09-03 |  6 months  |
|     crab     | 1946-02-13 | 1950-03-03 | 4.1 years  |
|    insect    | 1945-07-20 | 1946-02-13 |  7 months  |
|    insect    | 1944-02-10 | 1945-07-20 | 1.4 years  |
| invertebrate | 1941-11-27 | 1944-02-10 | 2.2 years  |
|     fish     | 1937-03-23 | 1941-11-27 | 4.7 years  |
|     crab     | 1933-03-01 | 1937-03-23 | 4.1 years  |
|     worm     | 1928-01-08 | 1933-03-01 | 5.1 years  |
|     fish     | 1923-05-09 | 1928-01-08 | 4.7 years  |
|     frog     | 1913-06-21 | 1923-05-09 | 9.9 years  |
|    insect    | 1912-07-23 | 1913-06-21 | 11 months  |
|    insect    | 1912-03-05 | 1912-07-23 |  5 months  |
|     crab     | 1908-03-29 | 1912-03-05 | 3.9 years  |
|    insect    | 1907-07-22 | 1908-03-29 |  8 months  |
|    insect    | 1907-05-01 | 1907-07-22 |  3 months  |
|     worm     | 1901-11-04 | 1907-05-01 | 5.5 years  |
|     crab     | 1897-10-15 | 1901-11-04 | 4.1 years  |
|    insect    | 1896-08-27 | 1897-10-15 | 1.1 years  |
| invertebrate | 1894-07-01 | 1896-08-27 | 2.2 years  |
|     fish     | 1889-11-05 | 1894-07-01 | 4.7 years  |
|    insect    | 1889-06-24 | 1889-11-05 |  4 months  |
|    insect    | 1887-07-26 | 1889-06-24 | 1.9 years  |
|    insect    | 1887-04-25 | 1887-07-26 |  3 months  |
|    insect    | 1887-04-14 | 1887-04-25 |  11 days   |
|     crab     | 1883-03-29 | 1887-04-14 | 4.0 years  |
|    insect    | 1882-06-26 | 1883-03-29 |  9 months  |
|     fish     | 1877-11-02 | 1882-06-26 | 4.6 years  |
|    insect    | 1877-10-11 | 1877-11-02 |  22 days   |
|     worm     | 1872-05-09 | 1877-10-11 | 5.4 years  |
|    insect    | 1869-08-21 | 1872-05-09 | 2.7 years  |
|    insect    | 1868-07-29 | 1869-08-21 | 1.1 years  |
|     worm     | 1862-12-31 | 1868-07-29 | 5.6 years  |
|    insect    | 1862-08-05 | 1862-12-31 |  5 months  |
|     dog      | 1854-09-09 | 1862-08-05 | 7.9 years  |
|     crab     | 1850-09-12 | 1854-09-09 | 4.0 years  |
|    insect    | 1850-01-26 | 1850-09-12 |  8 months  |
|    insect    | 1849-09-19 | 1850-01-26 |  4 months  |
|     fish     | 1845-01-16 | 1849-09-19 | 4.7 years  |
|    insect    | 1844-10-27 | 1845-01-16 |  3 months  |
|    insect    | 1843-12-05 | 1844-10-27 | 11 months  |
|    insect    | 1843-12-01 | 1843-12-05 |   4 days   |
|    insect    | 1843-07-31 | 1843-12-01 |  4 months  |
|     frog     | 1833-09-25 | 1843-07-31 | 9.9 years  |
|    insect    | 1832-12-10 | 1833-09-25 | 10 months  |
|    insect    | 1832-05-11 | 1832-12-10 |  7 months  |
|    insect    | 1831-10-26 | 1832-05-11 |  7 months  |
|    insect    | 1831-04-21 | 1831-10-26 |  6 months  |
|    insect    | 1831-02-20 | 1831-04-21 |  2 months  |
|     crab     | 1827-01-19 | 1831-02-20 | 4.1 years  |
|    insect    | 1826-04-27 | 1827-01-19 |  9 months  |
|    insect    | 1825-07-13 | 1826-04-27 | 10 months  |
|    insect    | 1825-03-07 | 1825-07-13 |  4 months  |
|    insect    | 1824-12-30 | 1825-03-07 |  2 months  |
| invertebrate | 1822-10-15 | 1824-12-30 | 2.2 years  |
|     crab     | 1818-10-22 | 1822-10-15 | 4.0 years  |
|    insect    | 1818-05-01 | 1818-10-22 |  6 months  |
+--------------+------------+------------+------------+


But what I found was that after considering this table of
past lives, I would see an insect landing on my face
(trying to collect water, I guess)
and I would instantly think
"this is what I may be born into" rather than
"what an annoyance this is."

So I think this kind of experience has to do with the Buddha
wanting you to view every kind of sentient being the same as
any every other kind of sentient being.

This is contrary to what we tend to do, which is separate
beings into various kinds of classes of beings, some of which
are acceptable to kill with a fly-swatter and others, which
aren't.