Special connection with animals

Im not sure how "buddhist" my answer is... but animals tend to be more sensitive to environmental factors so any change in you would be likely to have an impact on their reaction.

Mettanisansa Sutta lists eleven benefits of Metta meditation. Two of them are as follows:

• Manussanam Piyo Hoti: Pleasant to humans
• Amanussnam Piyo Hoti: Pleasant to non-humans.

So if you are practicing Metta, it could be the second benefit mentioned above.

I remember in Ajahn Maha Boowa's book, "Acariya Mun Bhuridatta A Spiritual Biography" he mentions that tigers weren't harming dhutanga monks in Thai forests while the villagers living nearby were not spared. In one section he mentions that one tiger was protecting a monk in a cave from other tigers during his meditation practice at nights.

In one of Ajahn Brahm's books he mentions how they had difficulties from mosquitos during their initial stages of practice and later as their meditation developed how the troubles became less and less.

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.